{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "52c53da4",
   "metadata": {},
   "source": [
    "# Analytic methods\n",
    "\n",
    "This book has focused on computational methods like simulation and\n",
    "resampling, but some of the problems we solved have analytic solutions\n",
    "that can be much faster.\n",
    "\n",
    "I present some of these methods in this chapter, and explain how they\n",
    "work. At the end of the chapter, I make suggestions for integrating\n",
    "computational and analytic methods for exploratory data analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f61641d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from os.path import basename, exists\n",
    "\n",
    "\n",
    "def download(url):\n",
    "    filename = basename(url)\n",
    "    if not exists(filename):\n",
    "        from urllib.request import urlretrieve\n",
    "\n",
    "        local, _ = urlretrieve(url, filename)\n",
    "        print(\"Downloaded \" + local)\n",
    "\n",
    "\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkstats2.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkplot.py\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "101a23bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import random\n",
    "\n",
    "import thinkstats2\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a66b3b13",
   "metadata": {},
   "source": [
    "## Normal distributions\n",
    "\n",
    "As a motivating example, let's review the problem from\n",
    "Section [\\[gorilla\\]](#gorilla){reference-type=\"ref\"\n",
    "reference=\"gorilla\"}:\n",
    "\n",
    "> Suppose you are a scientist studying gorillas in a wildlife preserve.\n",
    "> Having weighed 9 gorillas, you find sample mean $\\bar{x}=90$ kg and\n",
    "> sample standard deviation, $S=7.5$ kg. If you use $\\bar{x}$ to estimate\n",
    "> the population mean, what is the standard error of the estimate?\n",
    "\n",
    "To answer that question, we need the sampling distribution of $\\bar{x}$.\n",
    "In Section [\\[gorilla\\]](#gorilla){reference-type=\"ref\"\n",
    "reference=\"gorilla\"} we approximated this distribution by simulating the\n",
    "experiment (weighing 9 gorillas), computing $\\bar{x}$ for each simulated\n",
    "experiment, and accumulating the distribution of estimates.\n",
    "\n",
    "The result is an approximation of the sampling distribution. Then we use\n",
    "the sampling distribution to compute standard errors and confidence\n",
    "intervals:\n",
    "\n",
    "1.  The standard deviation of the sampling distribution is the standard\n",
    "    error of the estimate; in the example, it is about 2.5 kg.\n",
    "\n",
    "2.  The interval between the 5th and 95th percentile of the sampling\n",
    "    distribution is a 90% confidence interval. If we run the experiment\n",
    "    many times, we expect the estimate to fall in this interval 90% of\n",
    "    the time. In the example, the 90% CI is $(86, 94)$ kg."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8d4ead4",
   "metadata": {},
   "source": [
    "Now we'll do the same calculation analytically. We take advantage of the\n",
    "fact that the weights of adult female gorillas are roughly normally\n",
    "distributed. Normal distributions have two properties that make them\n",
    "amenable for analysis: they are \"closed\" under linear transformation and\n",
    "addition. To explain what that means, I need some notation.\n",
    "\n",
    "If the distribution of a quantity, $X$, is normal with parameters $\\mu$\n",
    "and $\\sigma$, you can write $$X \\sim Normal~(\\mu, \\sigma^{2})$$ where\n",
    "the symbol $\\sim$ means \"is distributed\" and the script letter $Normal$\n",
    "stands for \"normal.\"\n",
    "\n",
    "A linear transformation of $X$ is something like $X' = a X + b$, where\n",
    "$a$ and $b$ are real numbers. A family of distributions is closed under\n",
    "linear transformation if $X'$ is in the same family as $X$. The normal\n",
    "distribution has this property; if $X \\sim Normal~(\\mu,\n",
    "\\sigma^2)$, $$X' \\sim Normal~(a \\mu + b, a^{2} \\sigma^2) \\tag*{(1)}$$\n",
    "Normal distributions are also closed under addition. If $Z = X + Y$ and\n",
    "$X \\sim Normal~(\\mu_{X}, \\sigma_{X}^{2})$ and\n",
    "$Y \\sim Normal~(\\mu_{Y}, \\sigma_{Y}^{2})$ then\n",
    "$$Z \\sim Normal~(\\mu_X + \\mu_Y, \\sigma_X^2 + \\sigma_Y^2)  \\tag*{(2)}$$\n",
    "In the special case $Z = X + X$, we have\n",
    "$$Z \\sim Normal~(2 \\mu_X, 2 \\sigma_X^2)$$ and in general if we draw $n$\n",
    "values of $X$ and add them up, we have\n",
    "$$Z \\sim Normal~(n \\mu_X, n \\sigma_X^2)  \\tag*{(3)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d753c4a",
   "metadata": {},
   "source": [
    "## Sampling distributions\n",
    "\n",
    "Now we have everything we need to compute the sampling distribution of\n",
    "$\\bar{x}$. Remember that we compute $\\bar{x}$ by weighing $n$ gorillas,\n",
    "adding up the total weight, and dividing by $n$.\n",
    "\n",
    "Assume that the distribution of gorilla weights, $X$, is approximately\n",
    "normal: $$X \\sim Normal~(\\mu, \\sigma^2)$$ If we weigh $n$ gorillas, the\n",
    "total weight, $Y$, is distributed $$Y \\sim Normal~(n \\mu, n \\sigma^2)$$\n",
    "using Equation 3. And if we divide by $n$, the sample mean, $Z$, is\n",
    "distributed $$Z \\sim Normal~(\\mu, \\sigma^2/n)$$ using Equation 1 with\n",
    "$a = 1/n$.\n",
    "\n",
    "The distribution of $Z$ is the sampling distribution of $\\bar{x}$. The\n",
    "mean of $Z$ is $\\mu$, which shows that $\\bar{x}$ is an unbiased estimate\n",
    "of $\\mu$. The variance of the sampling distribution is $\\sigma^2 / n$.\n",
    "\n",
    "So the standard deviation of the sampling distribution, which is the\n",
    "standard error of the estimate, is $\\sigma / \\sqrt{n}$. In the example,\n",
    "$\\sigma$ is 7.5 kg and $n$ is 9, so the standard error is 2.5 kg. That\n",
    "result is consistent with what we estimated by simulation, but much\n",
    "faster to compute!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea501ca9",
   "metadata": {},
   "source": [
    "We can also use the sampling distribution to compute confidence\n",
    "intervals. A 90% confidence interval for $\\bar{x}$ is the interval between\n",
    "the 5th and 95th percentiles of $Z$. Since $Z$ is normally distributed,\n",
    "we can compute percentiles by evaluating the inverse CDF.\n",
    "\n",
    "There is no closed form for the CDF of the normal distribution or its\n",
    "inverse, but there are fast numerical methods and they are implemented\n",
    "in SciPy, as we saw in\n",
    "Section [\\[normal\\]](#normal){reference-type=\"ref\" reference=\"normal\"}.\n",
    "`thinkstats2` provides a wrapper function that makes the SciPy function\n",
    "a little easier to use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6746d20a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "def EvalNormalCdfInverse(p, mu=0, sigma=1):\n",
    "    return norm.ppf(p, loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96d84578",
   "metadata": {},
   "source": [
    "Given a probability, `p`, it returns the corresponding percentile from a\n",
    "normal distribution with parameters `mu` and `sigma`. For the 90%\n",
    "confidence interval of $\\bar{x}$, we compute the 5th and 95th percentiles\n",
    "like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "24e98507",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "85.88786593262132"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EvalNormalCdfInverse(0.05, mu=90, sigma=2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5c0f1b48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "94.11213406737868"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EvalNormalCdfInverse(0.95, mu=90, sigma=2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5131aba9",
   "metadata": {},
   "source": [
    "So if we run the experiment many times, we expect the estimate, $\\bar{x}$,\n",
    "to fall in the range $(85.9, 94.1)$ about 90% of the time. Again, this\n",
    "is consistent with the result we got by simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a60bc2c",
   "metadata": {},
   "source": [
    "## Representing normal distributions\n",
    "\n",
    "To make these calculations easier, I have defined a class called\n",
    "`Normal` that represents a normal distribution and encodes the equations\n",
    "in the previous sections. Here's what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e1a0928e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloaded nsfg2.py\n"
     ]
    }
   ],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/normal.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/nsfg2.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/hypothesis.py\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "a50af1ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Normal(object):\n",
    "\n",
    "    def __init__(self, mu, sigma2):\n",
    "        self.mu = mu\n",
    "        self.sigma2 = sigma2\n",
    "\n",
    "    def __str__(self):\n",
    "        return 'N(%g, %g)' % (self.mu, self.sigma2)\n",
    "\n",
    "    def Sum(self, n):\n",
    "        return Normal(n * self.mu, n * self.sigma2)\n",
    "\n",
    "    def __mul__(self, factor):\n",
    "        return Normal(factor * self.mu, factor**2 * self.sigma2)\n",
    "\n",
    "    def __divide__(self, divisor):\n",
    "        return 1 / divisor * self"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f93b2c3",
   "metadata": {},
   "source": [
    "So we can instantiate a Normal that represents the distribution of\n",
    "gorilla weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2ef7229c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normal(90, 56.25)\n"
     ]
    }
   ],
   "source": [
    "from normal import Normal\n",
    "\n",
    "dist = Normal(90, 7.5**2)\n",
    "print(dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e33ba377",
   "metadata": {},
   "source": [
    "`Normal` provides `Sum`, which takes a sample size, `n`, and returns the\n",
    "distribution of the sum of `n` values, using Equation 3:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5de85591",
   "metadata": {},
   "source": [
    "So we can compute the sampling distribution of the mean with sample size\n",
    "9:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "c027758f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_xbar = dist.Sum(9) / 9\n",
    "dist_xbar.sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7122f409",
   "metadata": {},
   "source": [
    "The standard deviation of the sampling distribution is 2.5 kg, as we saw\n",
    "in the previous section. Finally, Normal provides `Percentile`, which we\n",
    "can use to compute a confidence interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "e33ee8c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(85.88786593262132, 94.11213406737868)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_xbar.Percentile(5), dist_xbar.Percentile(95)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54c8288d",
   "metadata": {},
   "source": [
    "And that's the same answer we got before. We'll use the Normal class\n",
    "again later, but before we go on, we need one more bit of analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2d7def3",
   "metadata": {},
   "source": [
    "## Central limit theorem\n",
    "\n",
    "As we saw in the previous sections, if we add values drawn from normal\n",
    "distributions, the distribution of the sum is normal. Most other\n",
    "distributions don't have this property; if we add values drawn from\n",
    "other distributions, the sum does not generally have an analytic\n",
    "distribution.\n",
    "\n",
    "But if we add up `n` values from almost any distribution, the\n",
    "distribution of the sum converges to normal as `n` increases.\n",
    "\n",
    "More specifically, if the distribution of the values has mean and\n",
    "standard deviation $\\mu$ and $\\sigma$, the distribution of the sum is\n",
    "approximately $Normal(n \\mu, n \\sigma^2)$.\n",
    "\n",
    "This result is the Central Limit Theorem (CLT). It is one of the most\n",
    "useful tools for statistical analysis, but it comes with caveats:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b496c8e0",
   "metadata": {},
   "source": [
    "-   The values have to be drawn independently. If they are correlated,\n",
    "    the CLT doesn't apply (although this is seldom a problem in\n",
    "    practice).\n",
    "\n",
    "-   The values have to come from the same distribution (although this\n",
    "    requirement can be relaxed).\n",
    "\n",
    "-   The values have to be drawn from a distribution with finite mean and\n",
    "    variance. So most Pareto distributions are out.\n",
    "\n",
    "-   The rate of convergence depends on the skewness of the distribution.\n",
    "    Sums from an exponential distribution converge for small `n`. Sums\n",
    "    from a lognormal distribution require larger sizes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a64651d4",
   "metadata": {},
   "source": [
    "The Central Limit Theorem explains the prevalence of normal\n",
    "distributions in the natural world. Many characteristics of living\n",
    "things are affected by genetic and environmental factors whose effect is\n",
    "additive. The characteristics we measure are the sum of a large number\n",
    "of small effects, so their distribution tends to be normal."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3d89aae",
   "metadata": {},
   "source": [
    "## Testing the CLT\n",
    "\n",
    "To see how the Central Limit Theorem works, and when it doesn't, let's\n",
    "try some experiments. First, we'll try an exponential distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "c3c5b9d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeExpoSamples(beta=2.0, iters=1000):\n",
    "    \"\"\"Generates samples from an exponential distribution.\n",
    "\n",
    "    beta: parameter\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(np.random.exponential(beta, n)) for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e6d3d30",
   "metadata": {},
   "source": [
    "`MakeExpoSamples` generates samples of sums of exponential values (I use\n",
    "\"exponential values\" as shorthand for \"values from an exponential\n",
    "distribution\"). `beta` is the parameter of the distribution; `iters` is\n",
    "the number of sums to generate.\n",
    "\n",
    "To explain this function, I'll start from the inside and work my way\n",
    "out. Each time we call `np.random.exponential`, we get a sequence of `n`\n",
    "exponential values and compute its sum. `sample` is a list of these\n",
    "sums, with length `iters`.\n",
    "\n",
    "It is easy to get `n` and `iters` confused: `n` is the number of terms\n",
    "in each sum; `iters` is the number of sums we compute in order to\n",
    "characterize the distribution of sums.\n",
    "\n",
    "The return value is a list of `(n, sample)` pairs. For each pair, we\n",
    "make a normal probability plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "8f957be2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def NormalPlotSamples(samples, plot=1, ylabel=\"\"):\n",
    "    \"\"\"Makes normal probability plots for samples.\n",
    "\n",
    "    samples: list of samples\n",
    "    label: string\n",
    "    \"\"\"\n",
    "    for n, sample in samples:\n",
    "        thinkplot.SubPlot(plot)\n",
    "        thinkstats2.NormalProbabilityPlot(sample)\n",
    "\n",
    "        thinkplot.Config(\n",
    "            title=\"n=%d\" % n,\n",
    "            legend=False,\n",
    "            xticks=[],\n",
    "            yticks=[],\n",
    "            xlabel=\"random normal variate\",\n",
    "            ylabel=ylabel,\n",
    "        )\n",
    "        plot += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42166062",
   "metadata": {},
   "source": [
    "`NormalPlotSamples` takes the list of pairs from `MakeExpoSamples` and\n",
    "generates a row of normal probability plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "8955b2c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABR0AAAGgCAYAAAAn58BSAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy80BEi2AAAACXBIWXMAAA9hAAAPYQGoP6dpAAC/7ElEQVR4nOzdd3hb5fk+8Ftb8pBs2ZZleSTO3oMkJCEkBBIyCDMpLaPMtLQ0CSVpaRu+tJAyUlpGS8v4QSnQkYYywl5hJAEyIJOEDMj0kGV5SrKsrfP7w1jJseTEsiVr+P5cly/QezQe+4r1+Nx6z/tKBEEQQERERERERERERBQj0kQXQEREREREREREROmFoSMRERERERERERHFFENHIiIiIiIiIiIiiimGjkRERERERERERBRTDB2JiIiIiIiIiIgophg6EhERERERERERUUwxdCQiIiIiIiIiIqKYYuhIREREREREREREMcXQkYiIiIiIiIiIiGKKoSMRERERERERERHFFENHoj7gxRdfxA9/+EMMHjwYEokEM2fOTHRJREREZxRN//J4PPj1r38Nk8kEjUaDyZMnY/369b1XLBER0Sni1cM2b96Mc889FxkZGTAajbjtttvQ0tISp++CqGcYOhL1AU8++SRef/11lJaWIjc3N9HlEBERdUk0/evGG2/EI488gmuvvRZ/+ctfIJPJcNFFF+Gzzz7rpWqJiIhOikcP2717N2bNmoXW1lY88sgj+NGPfoSnn34aV155ZTy/FaJukwiCICS6CCKKr8rKShQXF0MqlWLUqFHIz8/Hhg0bEl0WERHRaXW1f33xxReYPHky/vSnP+GXv/wlAMDtdmPUqFEwGAzYvHlzL1dORER9XTx62EUXXYTdu3fj4MGD0Gq1AIC///3v+PGPf4z3338fc+bM6ZXvjairONORKAncc889kEgkOHz4MG688Ubk5ORAp9PhpptuQmtra4+fv7S0FFIpf92JiCi2kqV/vfzyy5DJZLjllltCY2q1GosXL8aWLVtQWVnZ41qIiCi9pFoPs9vtWL9+PX74wx+GAkcAuP7665GVlYX//e9/Pa6ZKNbkiS6AiE76/ve/j/LycqxevRo7d+7E3//+dxgMBjz44IMAAJvNBp/Pd8bnUavVyMrKine5REREABLfv3bt2oUhQ4aITsIA4OyzzwbQdjlaaWlp1M9LRETpL1V62N69e+H3+zFx4kTR/ZRKJcaNG4ddu3ZF/dpE8cbQkSiJjB8/Hs8++2zodkNDA5599tlQw7vsssuwcePGMz7PDTfcgOeffz5eZRIREYkkun/V1NSgqKgobLx9zGw2R/2cRETUN6RKD6upqRGNd7zvp59+GvVrE8UbQ0eiJPLTn/5UdHv69OlYt24d7HY7tFotHn74YTQ1NZ3xeUwmU7xKJCIiCpPo/uVyuaBSqcLG1Wp16DgREVEkqdLD2v/b2X3Z6ygZMXQkSiJlZWWi2+27nDU1NUGr1WLChAmJKIuIiOi0Et2/NBoNPB5P2Ljb7Q4dJyIiiiRVelj7fzu7L3sdJSOGjkRJRCaTRRxv32S+sbERXq/3jM+j0Wig0+liWhsREVFnEt2/ioqKUF1dHTbefikarwAgIqLOpEoPa7+sun28433Z6ygZMXQkSiELFy7kmo5ERJRy4t2/xo0bh08++SR0KVy7bdu2hY4TERF1R7L0sFGjRkEul2P79u34/ve/H7qf1+vF7t27RWNEyYKhI1EK4ZqORESUiuLdv773ve/hoYcewtNPP41f/vKXANouP3vuuecwefJk7lxNRETdliw9TKfTYfbs2fj3v/+N3/72t8jOzgYA/Otf/0JLSwuuvPLKbr0+UTwxdCRKId1dT2TTpk3YtGkTAKCurg5OpxP33XcfAGDGjBmYMWNGzGokIiLqKN79a/LkybjyyiuxcuVKWK1WDBo0CC+88AKOHz8u2pGUiIgoWsnUw+6//36cc845OO+883DLLbegqqoKDz/8MObMmYN58+b14Lskig+GjkR9wMcff4xVq1aJxn77298CAO6++26GjkRElJSi6V///Oc/8dvf/hb/+te/0NTUhDFjxuCtt95ijyMiooSIRw8766yz8OGHH+LXv/41li9fjuzsbCxevBirV6+O/zdE1A0SoX11VCIiIiIiIiIiIqIYkCa6ACIiIiIiIiIiIkovDB2JiIiIiIiIiIgophg6EhERERERERERUUwxdCQiIiIiIiIiIqKYYuhIREREREREREREMcXQkYiIiIiIiIiIiGJKnugCelMwGITZbEZ2djYkEkmiyyEiok4IggCHwwGTyQSplJ+PRcKeRkSUOtjXzox9jYgodXS1r/Wp0NFsNqO0tDTRZRARURdVVlaipKQk0WUkJfY0IqLUw77WOfY1IqLUc6a+1qdCx+zsbABtPxStVpvgaoiIqDN2ux2lpaWh920Kx55GRJQ62NfOjH2NiCh1dLWv9anQsX2avlarZSMjIkoBvLyqc+xpRESph32tc+xrRESp50x9jQuKEBERERERERERUUwxdCQiIiIiIiIiIqKYYuhIREREREREREREMdWn1nTsimAwCK/Xm+gy0p5CoYBMJkt0GUREaS8QCMDn8yW6jLSnVCohlfKzXCKieGNfiz+eqxFRrDB0PIXX68WxY8cQDAYTXUqfkJOTA6PRyAW1iYjiQBAEWCwWNDc3J7qUPkEqlaK8vBxKpTLRpRARpSX2td7FczUiigWGjt8RBAE1NTWQyWQoLS3lbIU4EgQBra2tsFqtAICioqIEV0RElH7aT8wMBgMyMjJ40hBHwWAQZrMZNTU1KCsr48+aiCgO2Nd6B8/ViCiWGDp+x+/3o7W1FSaTCRkZGYkuJ+1pNBoAgNVqhcFg4PR9IqIYCgQCoROzvLy8RJfTJxQUFMBsNsPv90OhUCS6HCKitMK+1rt4rkZEscLpfN8JBAIAwMuielF7uMs1WYiIYqv9fZUfovWe9r8f2v+eICKi2GFf6308VyOiWGDo2AGn6fce/qyJiOKL77O9hz9rIqL443tt7+HPmohigaEjERERERERERERxRRDR+qSmTNn4vbbb+/y/Z9//nnk5OTErR4iSk6CICAYDCa6DKIzYl8joq4KBoNoaGiAIAiJLoWoU+xrRNRVvkAQe8x2+IPx72vcSIaIiGKmoqYRv3jwJWRmqKDNVEObrcF9t13GS3SIiCglBQIB1NTUwO12w+v1wmg0sqcREVHKOt7owufHm+DwBOALCphYoovr6zF0JCKimLG3uCEAaGn1oKXVA7vTzZMzIiJKSYFAAGazGR6PBwDgdDpRW1uLwsJC9jYiIkopDo8fnx9rxvEmV2hsV7UDQ/IzoVXHLxrk5dURCIKAQCCQ0K+uXr4xc+ZMLFu2DLfffjtyc3NRWFiIZ555Bk6nEzfddBOys7MxaNAgvPvuu6HHbNy4EWeffTZUKhWKiorwm9/8Bn6/P3Tc6XTi+uuvR1ZWFoqKivDwww+Hva7H48Evf/lLFBcXIzMzE5MnT8aGDRt6/LMnotRmd7pFt7WZ6gRVQqdiX2NfI6Lo+P1+VFdXhwLHdi6XS/T+Qr0vlXoawL5GRIkVCArYWWXH2t0WUeDYfmzz8ea4vj5nOkYQDAZx7NixhNZQXl4OmUzWpfu+8MIL+NWvfoUvvvgCL774Im699VasW7cOV1xxBe688048+uijuO6661BRUYGmpiZcdNFFuPHGG/HPf/4TBw8exI9//GOo1Wrcc889AIA77rgDGzduxOuvvw6DwYA777wTO3fuxLhx40KvuXTpUuzfvx9r166FyWTCunXrMG/ePOzduxeDBw+Ow0+EiFKBo0UcOmZnaRJUCZ2KfY19jYi6rj1w9Pl8onGZTIbi4mIoFIoEVRYfq1evxquvvoqDBw9Co9HgnHPOwYMPPoihQ4eK7rdlyxb83//9H7Zt2waZTIZx48bh/fffh0bT1usbGxuxbNkyvPnmm5BKpVi0aBH+8pe/ICsrK6b1plpPA9jXiCgxqprd+PRYE2zuyB+WFWWrcHZZfC+v5kzHNDB27FjcddddGDx4MFauXAm1Wo38/Hz8+Mc/xuDBg/G73/0ODQ0N+Oqrr/DEE0+gtLQUf/vb3zBs2DBcfvnlWLVqFR5++GEEg0G0tLTg2WefxUMPPYRZs2Zh9OjReOGFF0SfrFVUVOC5557DSy+9hOnTp2PgwIH45S9/iXPPPRfPPfdcAn8SRJRodqf40zPOdKTuYF8jokTx+XyoqqoKCxzlcjmKi4uhVCoTVFn8bNy4EUuWLMHWrVuxfv16+Hw+zJkzB06nM3SfLVu2YN68eZgzZw6++OILfPnll1i6dCmk0pOnk9deey2+/vprrF+/Hm+99RY2bdqEW265JRHfUtJhXyOi3tTi8WP9N/V460BdxMBRo5DigkF6XDqyAPqM+H6QxpmOaWDMmDGh/5fJZMjLy8Po0aNDY4WFhQAAq9WKAwcOYOrUqaJ1aKZNm4aWlhZUVVWhqakJXq8XkydPDh3X6/WiTzr37t2LQCCAIUOGiOrweDzIy8uL+fdHRKnD0eHy6myGjtQN7GtElAherxdmszns8mmFQgGTyZR2Mxzbvffee6Lbzz//PAwGA3bs2IEZM2YAAJYvX47bbrsNv/nNb0L3O/V99MCBA3jvvffw5ZdfYuLEiQCAv/71r7jooovw0EMPwWQy9cJ3krzY14ioNwSCAvZZHNheaYevk52pRxqzcHapDip578xBZOiYBjr+ASSRSERj7Q0rGAzG5PVaWlogk8mwY8eOsMsKYn35BBGllo5rOuqyGDpS9NjXiKi3eTwemM1mBAIB0bhCoUBxcTHk8r5z2mSz2QC0BVlAWxC2bds2XHvttTjnnHNw5MgRDBs2DPfffz/OPfdcAG0zIXNyckKBIwDMnj0bUqkU27ZtwxVXXBH2Oh6PR7Rmpt1uj+e3lVDsa0QUbzV2Dz491oTGVl/E44YsJaaX56Igq3dn7Ped7hkFqVSK8vLyhNcQD8OHD8crr7wCQRBCze3zzz9HdnY2SkpKoNfroVAosG3bNpSVlQEAmpqa8M033+C8884DAIwfPx6BQABWqxXTp0+PS51ElJq4pmNyYl9jXyOizrndbpjN5rDAR6lUori4OKq1+1JdMBjE7bffjmnTpmHUqFEAgKNHjwIA7rnnHjz00EMYN24c/vnPf2LWrFnYt28fBg8eDIvFAoPBIHouuVwOvV4Pi8US8bVWr16NVatWRV1jOvc0gH2NiKK3x2zHlhO2iMdUcikml+kw3JApmkHdWxg6RiCRSNL2j4uf/exn+POf/4xly5Zh6dKlOHToEO6++26sWLECUqkUWVlZWLx4Me644w7k5eXBYDDg//7v/0SNdciQIbj22mtx/fXX4+GHH8b48eNRV1eHjz76CGPGjMGCBQsS+B0SUSJx9+rkxL7GvkZEkblcLtTU1IQFjiqVCiaTKW3fOzuzZMkS7Nu3D5999llorP1n85Of/AQ33XQTgLZQ66OPPsI//vEPrF69uluvtXLlSqxYsSJ02263o7S09IyPS+eeBrCvEVF0/EEBX1REnik+zJCJyWU6aBSJe89k6NjHFBcX45133sEdd9yBsWPHQq/XY/HixbjrrrtC9/nTn/6ElpYWXHLJJcjOzsYvfvGL0GUW7Z577jncd999+MUvfoHq6mrk5+djypQpuPjii3v7WyKiJBK2piMvr6Y4Y18jou5qbW1FTU0NBEG87pVarYbJZIrrbLZktHTp0tAGMCUlJaHxoqIiAMCIESNE9x8+fDgqKioAAEajEVarVXTc7/ejsbERRqMx4uupVCqoVKpYfgtpgX2NiKLh8gUQ6NDH8jIUmF6eC6M28e+xEqFjl01jdrsdOp0ONpsNWq1WdMztduPYsWMoLy+HWs2T5N7AnzlR+rn6l3+H13dyAf7Vy6/AkP6FUT/P6d6vqQ17WnLhz5wotTidTlgslrDAUaPRoKioKOaBYzL3NUEQsGzZMqxbtw4bNmzA4MGDw46XlJTg5ptvxr333hsaHz9+PObPn48HHngABw4cwIgRI7B9+3ZMmDABAPDBBx9g3rx5qKqq6tJGMuxryYU/c6LUYHP78N9d4mUsFp9dDIUsvh+cdbWvcaYjERHFhMfrEwWOAHevJiKi5NPS0oLa2tqwwDEjIwNGo7HPzXBcsmQJ1qxZg9dffx3Z2dmhNRh1Oh00Gg0kEgnuuOMO3H333Rg7dizGjRuHF154AQcPHsTLL78MoG3W47x58/DjH/8YTz31FHw+H5YuXYqrrrqqz+9cTUQUT5E2qZZJe3/txs4wdCQiophwOD1hY1peXk1EREnE4XCgtrY2bDwrKwuFhYUJWWQ/0Z588kkAwMyZM0Xjzz33HG688UYAwO233w63243ly5ejsbERY8eOxfr16zFw4MDQ/f/zn/9g6dKlmDVrFqRSKRYtWoTHHnust74NIqI+KdK1y8nUyRg6EhFRTHRcz1EqkSBDrUxQNURElAoEQcD6fbWYMigPWo0irq9lt9vD1h0EgOzsbBgMhj4ZOAIIm/HZmd/85jf4zW9+0+lxvV6PNWvWxKosIiLqgmCH93CpBEnVz/rWtQNERBQ3HXeuzs5SJ1XDIyKi5OLxBfDkR0fwv21VeOqjI/AHgmd+UDc1NzdHDBy1Wm2fDhyJiCi1dby8Otn6GUNHIiKKCUeLOHTUcj1HIiLqRL3Dg9VvHsTO480AgG8sLfjv1sq4vFZTUxPq6+vDxnU6HQoKCpLuBI2IiKirIs10TCYMHTvoQ5t5J1wwGL9Ps4mo99laXKLb3EQm8fg+23v49wNR131jceC+1w+gqlHcNzYdrENVY2vMXkcQBDQ2NqKhoSHsWG5uLvLz8xk4phj2td7DnzVRahCEtt9Xr9cLCAKkSdbXuKbjdxQKBSQSCerq6viJZ5wJggCv14u6ujpIpVIolVzzjSgddLy8mjMdE0epVEIqlcJsNqOgoABKpZJ9LY4EQUBdXR0kEgkUiviuSUeU6jYdrMN/Nlcg0OF6sAylDD+dNRAl+oyYvI4gCGhoaEBzc3PYMb1eD71eH5PXod7BvtZ7eK5GlFrcHg/cbnfoA3C1QpbgisQYOn5HJpOhpKQEVVVVOH78eKLL6RMyMjJQVlYGqZQTbonSQcfLq7O5c3XCSKVSlJeXo6amBmazOdHl9AkSiQQlJSWQyZLrDz2iZOEPBPG/bVX4eH/4uorGHDWWXTgIhbrY9A1BEFBfXw+bzRZ2LD8/Hzk5OTF5Heo97Gu9j+dqRMnP7XajttYaChx9Ph983uT6nWXoeIqsrCwMHjwYPp8v0aWkPZlMBrlczk8oidJI+ExHTYIqIaBtVkhZWRn8fj8CgUCiy0l7CoWCgSNRJ1rcfjz18REcNDvCjo0u1eHHM8uRoYrNaYkgCLBarXA4wl+roKAAOp0uJq9DvY99rffwXI0o+bndbpjNZgQ6LIUQDPoRDAaT5gMDho4dyGQynjQQEXWDw8k1HZNN++W+vOSXiBKlusmFv31wGHUOT9ixeWOMWDixGNIYrXovCAJqa2vR0tISdsxgMECr1cbkdShx2NeIiACXywWz2QxBEOA4Zc6cTCZDVmZm0gSOAENHIiKKEXvH3at5eTURUZ+250Qznt5wFB6feBaGXCbBDef2x9TBeTF7LUEQYLFY4HQ6w44ZjUZkZWXF7LWIiIgSpbW1FTU1NXD7g9jbGES1s+3SaplMBpVKBVmSbV/N0JGIiGLC0eHyas50JCLqmwRBwLt7LFi3oxodN3bPyVDgZ7MHYoAhdiFgMBiExWJBa6t452uJRAKj0YjMzMyYvRYREVGiOJ1O1NTUoMoZxN6GILzffabXHjhKJBIYs1WJLbKDpJlzuWnTJlxyySUwmUyQSCR47bXXRMdvvPFGSCQS0de8efMSUywREYkIgsDdq4mICP5AEM9uPIZXt4cHjv0LMnDXZcNjHjjW1NREDByLiooYOBIRUVpwOp04XlWDbdYAdtSJA0f1d4FjWY4a5/TLSWidHSXNTEen04mxY8fi5ptvxsKFCyPeZ968eXjuuedCt1Wq5EpwiYj6qla3F4GA+PI57l5NRNS3eHwBPPnREeyrsocdmzJIj+vP7Q+lPHZzHgKBQNslZm7xh14SiQQmkwkaDTc0IyKi1OdwOPDF4Rp83RTEqSuWyOVyqJRKqBQyTOufg8H5GUm3AVTShI7z58/H/PnzT3sflUoFo9HYSxUREVFXNdpaw8ZytRkJqISIiBLB4fbhsfcP41ideE1FiQRYOLEY88YYY3oiFAgEYDab4fGIN6iRSqUwmUxQq/nBFxERpb6ahmasP1CLOrf48oH2wLE8LwPTy3ORoUzODZGTJnTsig0bNsBgMCA3NxcXXHAB7rvvPuTlxW4BaiIi6p5muzh0zFAroVSkVIshIqJuqnd48Oh736DWJg4AFTIJfnrBQIyN8aVefr8fZrMZXq9XNC6TyWAymXg1FBERpTxBELD9WB02H2uEv8NyJXK5HLpMDaYPyMXAvOSe6JEyZ4Tz5s3DwoULUV5ejiNHjuDOO+/E/PnzsWXLFshkkRNdj8cj+vTTbg+/1IOIiHquY+io13ENLSKivqC6yYU/v/cNmpw+0XimSoafzx0c0/UbgbbAsbq6Gj6f+PVkMhmKi4uhVCpj+npERETx5vQGYHP70OoNotUbQKsvgOP1dlQ3hV9NppDLMbI4F9P650CtSM7ZjadKmdDxqquuCv3/6NGjMWbMGAwcOBAbNmzArFmzIj5m9erVWLVqVW+VSETUZzV2CB1ztFxHi4go3R2ubcFj73+LVm9ANJ6bqcDyeUNgyo1tL/D5fKiurobf7xeNy+VyFBcXQ6FQxPT1iIiI4u2zY03YZ2kRjfl8vrDZ/ACg1Shx4XAj+uuTe3bjqZJm9+poDRgwAPn5+Th8+HCn91m5ciVsNlvoq7KyshcrJCLqOzrOdMzheo5ERGltz4lmPPzOobDAsShHjZWXDI954Oj1elFVVRUWOCoUCgaORESUkqwt3i4HjsMNmbju7H4pFTgCKTTTsaOqqio0NDSgqKio0/uoVCqu6UJE1AuaOl5ereXl1URE6erLo4145pOjCHZYY2pQYRaWXjgIWerYnmJ4PB6YzWYEAuKAU6lUwmQyQS5P2VMaIiLqwyqaXSdvCAK8Pl/Y8iEZcuC8AbkYXmpIup2puyJpOnRLS4to1uKxY8ewe/du6PV66PV6rFq1CosWLYLRaMSRI0fwq1/9CoMGDcLcuXMTWDUREQFAk128WylnOhIRpSdBEPCvz0+EBY5jSnX4yawBUMlju76U2+2G2WxGMBgUjatUKphMpk7XdiciIkp21e0bsH0XOEqDPuSpJVDLALVMAq0SGFWSD0O+PrGF9kDShI7bt2/H+eefH7q9YsUKAMANN9yAJ598El999RVeeOEFNDc3w2QyYc6cObj33ns5k5GIKAk0212i27lc05GIKC05PQG0esQzDqcNycP15/aHTBrbGRgulws1NTUMHImIKO34AkHUOjyiGY6TDVIYM06ugpifn4+cnJzEFRkDSRM6zpw5E4IgdHr8/fff78VqiIgoGh0vr87l5dVERGkpGOHv9SvPLo154Nja2oqampqw8wO1Wg2TyQSpNGWXpiciIkKtw4tgUIDX64XP74cEQJ76ZC8tKCiATqdLXIExkjShIxERpSavzw+nyyMa4+XVRETpKdDxumoAMc4b4XQ6YbFYwgJHjUaDoqIiBo5ERJTyqmxueLze0AZpOSoJFN81VIPBAK1Wm8jyYoahIxER9UizwxU2lsvQkYgoLUUKHWM5y7GlpQW1tbVhgWNmZiYKCwsZOBIRUcpr8fjxVWVDKHAEgILvZjkWFhYiOzs7UaXFHENHIiLqkeYOl1bL5TJkapQJqoaIiOIp0uXV0hiFjg6HA7W1tWHjWVlZKCwsTMldO4mIiE7l9gXw8o4KONziXaoLNBIYjUZkZWUlqLL4YOhIREQ90mgT71ydm53BE0MiojQjCAJsrT4cr28NOyaLwXu+3W6H1WoNG8/OzobBYGBfISKilOcLBPHqzhNoaPWKxvPVEozqX5R2gSPA0JGIiHqo487VOdy5mogo5bV6/NhwsA5HrU5Y7W7U2T3wBSJv+tjTPLC5uRn19fVh41qtFgUFBQwciYgo5fkDAby+8wRqHOLAMUshwcWjTWkZOAIMHYmIqIeaHOJZL3odd64mIkp1z2w4hr2VtjPeTyGT9CgUbGpqQkNDQ9h4Tk4O8vLyGDgSEVHKCwQCePerCpywiQNHtVyCK8aYkKdLnzUcO2LoSEREPdLU4fLqnGxuIkNElMpO1Du7FDgCwOhSXbdeQxAENDY2oqmpKexYbm4u9Ho9A0ciIkppgiCgstmFzd/UoNohXsNRIZXg8tFFMOSmb+AIMHQkIqIe4uXVRETpZePBuk6PyWUS5GerYMhWYYAhE7NGFkb9/IIgoKGhAc3NzWHH8vLykJubG/VzEhERJVKLx4/9tU40uXwQhLaN12xuHyxNLQgGg6L7SiUSXDyqCMV52gRV23sYOhIRUY/w8moiovTh8gaw7UijaOycwXmYNiQfBdkq5GYqejQDURAE1NfXw2YLn0mZn5+PnJycbj83ERFRbxIEAS3eAJpdfrx9oC7smNvtDgscJRIJ5g0vxABD+geOAENHIiLqoWa7OHTM0fLyaiKiVLXtSAM8vpMnSFIJcMXEYuRmKnv83IIgwGq1wuFwhB0rKCiATte9S7WJiIh6g8cfxK5qOxpbfWjxBmBz+xEIhm+y1lngqJRJMGtoIYabcnqp4sRj6EhERN0mCAKaHeLLq3O5piMRUcradFC8i/TYspyYBY61tbVoaWkJO1ZYWIjs7PRe04qIiFJbi8ePtw/Uo8nlO+39IgWOWQoJBuXIMGVICTI16niXmlQYOhIRUbcdq6oP+wQvV8fQkYgoFTU5vahoEM9enzGsoMfPKwgCLBYLnE5n2DGj0YisrKwevwYREVG8NLX68NaBOji9gdPeTxAEuF0uZCmAkkwppBJAq5DAmCVHcXExlMqef4iXahg6EhFRt23dc0x0uzBPi1xeXk1ElJIOmsWXPWcoZRhZ3LM1p4LBICwWC1pbxWGmRCKB0WhEZibXASYiouTl8gXwxn4rXL5gp/dRSCXIVkkBTyuM+RKYMqWhY3J5W+CoUCh6o9ykw9CRiIi6bdtX4tBx8pjyHm0wQEREifPFUfEGMkOKsiGVdv89PRgMoqamBi6XeBkOiUSCoqIiZGTwQyoiIkpux5tcYYGjUibB+GItCrOVyFErIEcAZrMZfj8AnAwcFQoFTCZTnw0cgVN/GkRERFGotDShqrZJNDZ13IAEVZPc/vCHP0AikeD2228PjbndbixZsgR5eXnIysrCokWLUFtbm7giiajPsrt8eHFrJfZWineUHlbU/XUWA4G2E7COgaNUKoXJZGLgSEREKcHlFQeOOrUcV48vwvhiLUxaNeQIoLq6Gv62xDFEoVD06RmO7Rg6EhFRt3Sc5ZirzcDgfoYEVZO8vvzyS/y///f/MGbMGNH48uXL8eabb+Kll17Cxo0bYTabsXDhwgRVSUR91RdHGvHrtV9h/b7wDz2GmboXOrYHjm63WzTeHjhqNJpuPS8REVFv8wbEoaMhSwmNQgYA8Hg8qK6uRiAgXutRqVSiuLgYcjkvLmboSERE3bJ1z1HRbV5aHa6lpQXXXnstnnnmGeTm5obGbTYbnn32WTzyyCO44IILMGHCBDz33HPYvHkztm7dmsCKiagvOWptwbMbj8EXEMKOjSjWojg3+nDQ7/ejuroaHo9HNC6TyVBcXAy1um/t2klERKmtsVW8W7VS3hajeTwemM3msMBRpVIxcDwFQ0ciIoqatdGBY1X1orEpY3lpdUdLlizBggULMHv2bNH4jh074PP5ROPDhg1DWVkZtmzZ0ttlElEf1OL246mPjyIQFAeOcqkEF48rwtILB0X9QZLP50N1dTW8Xq9ovD1wVKlUPa6biIioN/gCQby2rxYVzeJZ+yqZFG63O+IMR5VKBZPJBJlM1pulJjVGr0REFLWOsxyzMlQYMbAoQdUkp7Vr12Lnzp348ssvw45ZLBYolUrk5OSIxgsLC2GxWCI+n8fjEc0cstvtMa2XiPoOQRDwj43H0NgiDgeHm7Jx3bn9YNBGPxuxPXDsuKZVX9+1k4iIUtOeGgcsDm/YuEbatoRIMCi+7FqtVsNkMkEq5dy+U/GnQUREUdu6R7ye49mjyyGTsaW0q6ysxM9//nP85z//idmlhKtXr4ZOpwt9lZaWxuR5iajvefnLKnzVYdOYIcYs3D5vSLcCR6/Xi6qqqoiL6JeUlDBwJCKilBEICqhocmF7ZfgH/MFAAEJLY1jgqNFoGDh2gj8RIiKKSqPNiW+OiWfjTRlbnqBqktOOHTtgtVpx1llnQS6XQy6XY+PGjXjssccgl8tRWFgIr9eL5uZm0eNqa2thNBojPufKlSths9lCX5WVlb3wnRBRutl0sA7vfyXeNCZbLcct5w+ATBr9urxcRJ+IiNJFvdOLF/dY8M7B+rBjgUAAgzN9yOjQ1jIyMlBUVMTAsRP8qRARUVS++Oo4Tl0BTK1SYMyQkoTVk4xmzZqFvXv3Yvfu3aGviRMn4tprrw39v0KhwEcffRR6zKFDh1BRUYGpU6dGfE6VSgWtViv6IiKKxv5qO/6zuUI0JpNKcMsFA5CTqYz6+U63phUDx9SxevVqTJo0CdnZ2TAYDLj88stx6NChiPcVBAHz58+HRCLBa6+9JjpWUVGBBQsWICMjAwaDAXfccUfY7FciomRlc/vwxtd1sLvD37eCgQBmF/pRni3+cC4jIwNGo5GB42nwLwEiIorKtq/El1ZPGNkPCgUXSz5VdnY2Ro0aJRrLzMxEXl5eaHzx4sVYsWIF9Ho9tFotli1bhqlTp2LKlCmJKJmI0py5yYWnPjoStnHMdef2w3BT9B9iuFwu1NTURFzTqqioiIvop5CNGzdiyZIlmDRpEvx+P+68807MmTMH+/fvR2Zmpui+f/7znyNuMBQIBLBgwQIYjUZs3rwZNTU1uP7666FQKPDAAw/01rdCRNQtDo8fr++rgzcQDDvm9/thUvkgk4iDxczMTBiNxqg3XetrGDoSEVGX+f0BfH3ELBqbyl2ru+XRRx+FVCrFokWL4PF4MHfuXDzxxBOJLouI0pDd5cNjH3yLVq94RuL8sUacOyQ/6udrbW1FTU0NBEEcYGo0Gl5iloLee+890e3nn38eBoMBO3bswIwZM0Lju3fvxsMPP4zt27ejqEi8edwHH3yA/fv348MPP0RhYSHGjRuHe++9F7/+9a9xzz33QKmMfiYtEVFv2XrChlafuEdmKGQwZkig8rlgyhAHi1lZWSgsLGTg2AUMHYmIqMsabE4EOnwCOGqwKUHVpJYNGzaIbqvVajz++ON4/PHHE1MQEfUJXn8Qj68/jPoOO3BOKM/FwonFUT+f0+mExWIJCxx5iVn6sNnaNhnS6/WhsdbWVlxzzTV4/PHHI649vGXLFowePRqFhYWhsblz5+LWW2/F119/jfHjx8e/cCKibnB6Azje5BKN6dRyzC3PRGO9FVCK+1r7UhQMHLuGoSMREXVZXaNDdFulVCArQ5WgaoiI6EzWbq3AEatTNFZekInF55VHfcLU0tICi8USNs5LzNJHMBjE7bffjmnTpomWCVm+fDnOOeccXHbZZREfZ7FYRIEjgNDtSP9mgLZNiDweT+i23R6+UywRUTy5fAF8cKg+bOmRGSXqtsCxA61Wi4KCAva7KDB0JCKiLqtvahHdNuiz2HSJiJLUQbMdmzrswKnPUmLphYOglEc3I9HhcKC2tjZsnJeYpZclS5Zg3759+Oyzz0Jjb7zxBj7++GPs2rUrpq+1evVqrFq1KqbPSUTUVdU2Nz76tjHssuqybClctoaw++t0OuTn57PfRYnXPxARUZfVdQgd83OzElQJERFFEgwKqGl24d09NXjsg8Nhx38+ZzB0GYqontNms0UMHLOzsxk4ppGlS5firbfewieffIKSkpLQ+Mcff4wjR44gJycHcrk8tCv5okWLMHPmTACA0WgM+zfSfjvS5dgAsHLlSthsttBXZWVlHL4rIqJwVTY33txfFxY4SoN+9FO0ht0/JyeHgWM3caYjERF1WcfLqxk6EhElnj8QxNfVdmw73Ig9lc3w+MJ33wSAWSMNKNZronru5uZm1NfXh41zxkf6EAQBy5Ytw7p167BhwwaUl5eLjv/mN7/Bj370I9HY6NGj8eijj+KSSy4BAEydOhX3338/rFYrDAYDAGD9+vXQarUYMWJExNdVqVRQqbhECxH1vs3Hm8PGpEE/xun8UMnEfS03Nxd6vZ79rpsYOhIRUZd1vLy6QJ+doEqIiKjZ6cW7X1nwxZFGONz+0953RLEWCydFt3FMY2MjGhsbw8ZzcnKQl5fHE7A0sWTJEqxZswavv/46srOzQ2sw6nQ6aDQaGI3GiLMVy8rKQgHlnDlzMGLECFx33XX44x//CIvFgrvuugtLlixhsEhESaWp1YfGVt/JAUFAnkrA8Cw/1B0CR71eL9pUi6LH0JGIiLqs40zHAs50JCJKCI8/gD++fQhWu+eM9508UI8bZ/SHQta1lZUEQUBjYyOamprCjun1euTm5jJwTCNPPvkkAIQulW733HPP4cYbb+zSc8hkMrz11lu49dZbMXXqVGRmZuKGG27A73//+xhXS0TUM+8dOmX2viBAJgQwTusP62t5eXnIzc3t5erSD0NHIiLqEkEQIqzpyJmORESJ8Nmh+tMGjjkZCgw2ZuHCUYUYYOj6B0SCIKChoQHNzc1hx3gClp4EQTjznbrwmH79+uGdd96JRUlERHHxwvZquNqXIBEEeL1elGYEIZGIP5TLz89HTk5O7xeYhhg6EhFRl9hb3PD5xYstc6YjEVFi7K+2h40NMGRiyqA8nNUvBzmZyqifUxAE1NXVwW4Pf26egBERUSqrd3pFgaPH64Xf70dxhkx0v4KCAuh0ugRUmJ4YOhIRUZd0XM9RAkCvy0xMMUREfVxFg3h3zUvGF+GyCdGt2XgqQRBgtVrhcDjCjhkMBmi12m4/NxERUSL5AkG88XVd241TAkeNHMg9ZdlZ9rvYY+hIRERdUtckPhHV52RC1sX1wYiIKHbsLh+anD7R2KQB3V/oXhAE1NbWoqWlJexYYWEhsrO5lAYREaUmQRCw6WgTvIGgKHAEgNnFstBajux38cHQkYiIuqSukTtXExElgxP14lmOSrkURp26W88VDAZRW1sLp9MpGpdIJCgsLERWFpfRICKi1NTY6sP/9ljabnQIHMfmSSGVSNjv4oyhIxERdUnHy6vzuZ4jEVFCVHa4tLpUr4FUGv1u0sFgEDU1NXC5XKJxiUQCo9GIzEwuoUFERKmp2SUOHN0eDwKBtvXptUoJSjMl7He9gKEjERF1SX2Hy6sLchg6EhElwokOoWNZfkbUzxEMBmE2m+F2u0XjEokERUVFyMiI/jmJiIiSxd6atgkTgiDAc0rgOFArxchcCaRSKftdL2DoSEREXVLXxMuriYiSQUWHy6vL8qI7YQoEAjCbzfB4PKLx9hMwjUbT4xqJiIgSyWx3hwWOY/Ok6J8t5QdsvYihIxERdUnH0JGXVxMR9b5Wjx91DnFY2C+/65eFBQIBVFdXw+v1isalUilMJhPU6u6tDUlERJQs3L4AGlt9cLvdCAaDAIDR+rbAkR+w9S6GjkREdEZenx/2FvGaX5zpSETU+yo6XFotl0pgyulaUOj3+2E2m8MCR5lMBpPJBJVKFbM6iYiIEsVsc4sCR5kE6J8t4QdsCcDQkYiIzqjjLEcAyOeajkREvc5iE6/BaMrVQC6TnvFxPp8PZrMZPp9PNC6Xy2EymaBUKmNaJxERUW8LCgL2mu34+FBtKHAEgCyFBHKZDMXFxfyArZcxdCQiojPquHN1hlqJDA1PUImIeltDi3iWYl72md+LfT4fqqur4ff7ReNyuRzFxcVQKBQxrZGIiCgRNh9rwpfH60WBIwCo5BIGjgnC0JGIiM6osdkpup3H9RyJiHpVq8ePPRU2vLvHIhrXZ54+dPR6vaiurg4tot9OoVCguLgYcjlPB4iIKPXtM9siBo4SiQRjygwMHBOEf2UQEdEZNdo7hI66rm9aQEREPdPk9OL+1w+gudUXdqz0NDtXezwemM3msMBRqVTCZDIxcCQiopQmCAKaXX7sMduw60QDgoIgOp6hkOK8IYUYUaRLUIXEvzSIiOiMOs50zNV1fpJLRESxtf1YU8TAsVCnwqQBuREf43a7YTabwy8xU6lgMpkgk8niUisREVFvqLa58fnxZtS3eOB2uyF0CByNmTIsPKsfNCouCZVIDB2JiOiMmuzi3VI505GIqPc0dljHEQBUCil+NnsQVPLw8NDlcsFsNoedgKnVahQVFTFwJCKilOXxB7Gr2o49ZgcCwWDEwFGjkGLRhP5QK7lmcaIxdCQiojNq6DDTUc/QkYio1zjc4bMcf33xMBTnasLGW1tbUVNTE34CptGgqKgIUumZd7omIiJKRk5vAK/tq4XDE0Cwk8Cxv06BWSNKGDgmCYaORER0Ro22DqFjDkNHIqLeIAgCDtU4RGNXTSlFWYS1HJ1OJywWS9gJWEZGBoxGIwNHIiJKabuq7REDR40cyFdLMESvwuiBpZzRn0QYOhIR0WkFg0E0d7i8Wq9l6EhE1Buqm1xocopnOo4s0Ybdr6WlBRaLJWw8MzMTRqMREokkbjUSERH1hmqbJyxwHKyTYniOBGq1mmsWJyGGjkREdFrNDlfYTnCc6UhE1Du+qrSJbudnK2HUqUVjdrsdVqs17LFZWVkoLCxk4EhERCnP5QugvsUNj8cTChxH5koxSCflmsVJjKEjERF1yu3x4d9vbhONSaVS5GSHryNGRESx9/HX4jBxdKlOFCLabDbU1dWFPU6r1aKgoICBIxERpbwmlw9rdlSLAkcAMGhOznDkEiLJiaEjERFFdMLcgIefW49qa7No3KDP4kksEVGceXwBvPRFFZpbO1xaXawL/X9zczPq6+vDHqvT6ZCfn8/3aiIiSmm+QBA2tx8v7jLD7XaLjmnkgEGrYeCY5Bg6EhERgLbNCjxeP2wtLuzcX4HnX9sCvz8Qdr8F541OQHVERH3L058cxZ4KW9h4UU7bpdWNjY1obGwMO56Tk4O8vDwGjkRElLJq7B5sOdEMa4sXgUAgLHAEgMnFmQwcUwBDRyKiPqDR5sTRqnrYHS40O1xwON2wtbhgb3HB1uJu+6/DBV+EkLGdSqnAz646D+dOGNSLlRMR9T31Dk/EwHF8vxwYtCo0NDSgqakp7Lher0dubi4DRyIiSllmuxtvfN22bEjA74fb4wm7z/SyTJw1qIT9LgUwdCQiSnMfbz2IJ/67AcKZ79qp8pJ8/OLGC1FUoDvznYmIKGrNTi+O1jnxraUF6/fVio7JZRJcMaEYs0YaUF9fD5stPJDMy8tDbm5ub5VLREQUcy5fIBQ4+v1+eCIEjqMMGkwazMAxVTB0JCJKcy+9v6NHgeNFM0bh+kunQqHgbnBERLFmd/nw/KbjYbtUn2rSAD3mjC5EXV0d7HZ72PGCggLodPxQiIiIUldFkwvvHGxbp7hj4KiWARlyCQblazBtKAPHVMLQkYgojQmCgLpGR9SPk8mkGFCSj0VzzsKkUf1jXxgRESEQFPDEh0dwuLbltPebNjgPVqsVDkf4+7nBYIBWq41XiURERHG3x2zHlhNtH751DBxnFMmQq5IgOzsbBoOBgWOKYehIRJTGWt3esFmOIweZkJeTCW2mBrpsDXTZamRnapCTrUF2phq6LA00agUbOhFRnO060XTawNGYo8b8MUboJE44HM6w44WFhcjOzo5niURERHH1taUlFDj6fD54vd7QsQn5UuSqJNBqtSgoKOD5SQpi6EhElMacLm/Y2G9+NA8ZGmUCqiEionZ7TjTjqY+Oho2PKNZioCETE8pzUaRToba2Fk5nq+g+EokEhYWFyMrK6q1yiYiIYsofFPDJ4QYcaXABCA8cJxVIYcqUQqfTIT8/n4FjikqavcU3bdqESy65BCaTCRKJBK+99prouCAI+N3vfoeioiJoNBrMnj0b3377bWKKJSJKcoIgwNrowI6vT4jGpRIJNGpFgqoiIiIAaGzx4smPj4SNXzGxGCvmD8FlE4phylHDYrGgtTU8cDQajQwciYgopX1+rCli4NgvS4JL+slgypQiNzeXgWOK6/FMR7vdjo8//hhDhw7F8OHDu/08TqcTY8eOxc0334yFCxeGHf/jH/+Ixx57DC+88ALKy8vx29/+FnPnzsX+/fuhVqt78i0QEaUsQRDg8fpRU2fD8eoGHKuux7GqehyvbkCrO3yWY4ZGyabdRbHqb0REHW08WAd/QLz4hUQCjO+XAwAIBoMwm81wu90d7iOByWSCRqPprVIpRbBnEVEq2VVtxwFr27IhXq8XPp8PAFCeLcFovRQSiQS5ubnQ6/U8d0lxUYeO3//+9zFjxgwsXboULpcLEydOxPHjxyEIAtauXYtFixZ1q5D58+dj/vz5EY8JgoA///nPuOuuu3DZZZcBAP75z3+isLAQr732Gq666qpuvSYRUSr75ngtnnpxE06YG7r8GL0uM44VpbZ49TciolMdq3Pi7d01YeO3nD8AplwNAoEAzGazaBF9AJBKpTCZTPywnQCwZxFR6vqiwoad1XZAEOD1+UKB47g8KcqyJJBIJNDr9dDr9QmulGIh6surN23ahOnTpwMA1q1bB0EQ0NzcjMceewz33XdfzAsEgGPHjsFisWD27NmhMZ1Oh8mTJ2PLli1xeU0iomT35NqNUQWOADB32sg4VZP6EtHfiKjvefmLqrCxX140BJMG6BEIBFBdXR0xcCwuLmbgSCHsWUSUily+QMTAsThTgn7ZbTMc8/PzGTimkahDR5vNFvoH8N5772HRokXIyMjAggUL4rbGosViAdC2Q9+pCgsLQ8ci8Xg8sNvtoi8ionTQZG9FRU3jGe+XqVFh1GATLj5vDO697TLMm87QsTOJ6G9E1LfYXT58Y3GIxnIzFRhalA2/34+qqirRIvoAIJPJUFxcDJVK1ZulUpJjzyKiVPTibktb4HjKJdUAMEbfFk0VFBQgJycnQdVRPER9eXVpaSm2bNkCvV6P9957D2vXrgUANDU1Jd2nr6tXr8aqVasSXQYRUcwdq6oPGyvIzcbA0nz0K85DeUk+yovzkZeTyXVQuiiV+hsRpaYvjzZCEC/liJ/PHQy/3w+z2Sw6AQMAuVwOk8kEpVLZi1VSKmDPIqJUIggCtlXY4PYF4PF64ff7Q8fml8qglElgMBig1WoTWCXFQ9Sh4+23345rr70WWVlZKCsrw8yZMwG0TfEfPXp0rOsDABiNRgBAbW0tioqKQuO1tbUYN25cp49buXIlVqxYEbptt9tRWloalxqJiHpTfVOL6LapQIe/3nV1gqpJD4nob0TUt7y1S7yW44TyXBiy5KiurhadgAFtgWNxcTEUCkVvlkgpgj2LiFLJ2wfqUdXsCgscx+ilUMokKCwsRHZ2dgIrpHiJOnT82c9+hrPPPhuVlZW48MILIZW2TYMdMGBA3NYPKS8vh9FoxEcffRQKGe12O7Zt24Zbb72108epVCpeikJEacnnD4hu63O4QUxPJaK/EVHf0ez0wuEWB4sjTZmorq5GICB+T1coFCguLoZcHvWf6tRHsGcRUao43uiKGDhmKyTol83AMd116y+ZiRMnYsyYMTh27BgGDhwIuVyOBQsW9KiQlpYWHD58OHT72LFj2L17N/R6PcrKynD77bfjvvvuw+DBg1FeXo7f/va3MJlMuPzyy3v0ukREqcjrE5+4KuSyBFWSXuLR34iIAKDG5hbdDgaDMMha0CFvhFKphMlkYuBIZ8SeRUTJTBAEvLrXiroWD9wej+gDtlyVBDOKZDAajcjKykpglRRvUW8k09raisWLFyMjIwMjR45ERUUFAGDZsmX4wx/+0O1Ctm/fjvHjx2P8+PEAgBUrVmD8+PH43e9+BwD41a9+hWXLluGWW27BpEmT0NLSgvfee49rlhBRn9RxpqNSwZPTnopXfyMiAoA6+8kdqYPBAFTwQd7hL3GVSsUZjtQl7FlElOy2V9lhjRA4AsCMIhmKiooYOPYBUYeOK1euxJ49e7BhwwZR4Dd79my8+OKL3S5k5syZEAQh7Ov5558HAEgkEvz+97+HxWKB2+3Ghx9+iCFDhnT79YiIUpnfHxTdlnOmY4/Fq78REQFArb1tpmMgEIDb7YZJJ16rUa1Ww2QyQSbj+zmdGXsWESUzty+A7ZU2eCIEjrNL2jZJy8zk8lB9QdQfo7722mt48cUXMWXKFNGOqCNHjsSRI0diWhwREUXGy6tjj/2NiOJFEAQcqXUiEAjA43FDEIC8zJPv2xqNBkVFRaF1+YjOhD2LiJKRIAj4pq4VHx9uiBg4ziiSY0i/Ymg0mgRVSL0t6tCxrq4OBoMhbNzpdIoaHhERxY/X1/HyaoaOPcX+RkSx5A8E8cqX1fiqshlNTh9cHi88Hg8Eoe14Xmbbn+EZGRkwGo0MHCkq7FlElGxONLnw7sF6CIIAt9uNYPDklVkaOTCvTImioiIGjn1M1H/dTJw4EW+//XbodntT+/vf/46pU6fGrjIiIupU2JqOXP+rx9jfiCiWXvqiCuv31aLW5kGr2wu3+2TgCAClOUpkZmZyhiN1Syx71urVqzFp0iRkZ2fDYDDg8ssvx6FDh0LHGxsbsWzZMgwdOhQajQZlZWW47bbbYLPZRM9TUVGBBQsWICMjAwaDAXfccYdop1oiSl/1Tm+ngaNEAkwoaLukmoFj3xP1WeoDDzyA+fPnY//+/fD7/fjLX/6C/fv3Y/Pmzdi4cWM8aiQiog46ho6KjrsRUNTY34goVo5aW/DxfisAwO/3wePxio6X5igxoCgXhYWFnJVG3RLLnrVx40YsWbIEkyZNgt/vx5133ok5c+Zg//79yMzMhNlshtlsxkMPPYQRI0bgxIkT+OlPfwqz2YyXX34ZQNtapQsWLIDRaMTmzZtRU1OD66+/HgqFAg888EA8fgRElCQEQcDLX9VGDBzVMmCKUY5RA0qhUqkSWCUlStRnqeeeey52794Nv9+P0aNH44MPPoDBYMCWLVswYcKEeNRIREQd+Dqs6Sjn5dU9xv5GRD21v9qOJz48jAffOgRBCA8cFTIJRps0+Mn5/Rg4Uo/Esme99957uPHGGzFy5EiMHTsWzz//PCoqKrBjxw4AwKhRo/DKK6/gkksuwcCBA3HBBRfg/vvvx5tvvhmayfjBBx9g//79+Pe//41x48Zh/vz5uPfee/H444/D6/We7uWJKMV9UWmLGDgO0kpxfomSgWMf163r8QYOHIhnnnkm1rUQEVEX+TrsXs3Lq2OD/Y2IumNvpQ1/ef9b0ZjP5wuFLUMMalw6KgdatRQ5OTnIz89n4Eg9Fq+e1X7ZtF6vP+19tFot5N/9/bFlyxaMHj0ahYWFofvMnTsXt956K77++muMHz8+5nUSUeI1tvqws8oOt8uF4ClriEwvkqEgQ47i4mIolcoEVkiJFvVZakVFxWmPl5WVdbsYIiLqGq+fu1fHGvsbEXXHvqqOgaPwXeDoAwAUaRW4ZoIeMqkEubm50Ov1DBypx+LVs4LBIG6//XZMmzYNo0aNinif+vp63HvvvbjllltCYxaLRRQ4AgjdtlgsEZ/H4/HA4/GEbtvt9m7VTESJ8U2dEx9+Uw+P2y0KHEsyJTBkKlBcXAyFQpHACikZRB069u/f/7R/KHXcEp2IiGIvfE1Hho49xf5GRN3xxk7zKbcEeL0++Hw+KGQSjC3WYO4wHWRSCfR6PXJzcxk4UkzEq2ctWbIE+/btw2effRbxuN1ux4IFCzBixAjcc8893XqNdqtXr8aqVat69BxE1PsEQcA7B+txorEVbrcbwqm7pAGYXKRi4EghUYeOu3btEt32+XzYtWsXHnnkEdx///0xK4yIiDrn83XYvZprOvYY+xsRRUsQBFTUt7bfgtfrhc/nx6giDS4dnQONom359Pz8fOTk5CSsTko/8ehZS5cuxVtvvYVNmzahpKQk7LjD4cC8efOQnZ2NdevWiQIFo9GIL774QnT/2tra0LFIVq5ciRUrVoRu2+12lJaWdqt2Iuo9J5rcnQaO04tVKCkpCS29QBT1v4SxY8eGjU2cOBEmkwl/+tOfsHDhwpgURkREnfP6O4aObOw9xf5GRNE6Xt8Kf1AAIMDj8cLv92PJdAOM2pNhTEFBAXQ6XeKKpLQUy54lCAKWLVuGdevWYcOGDSgvLw+7j91ux9y5c6FSqfDGG29ArVaLjk+dOhX3338/rFYrDAYDAGD9+vXQarUYMWJExNdVqVTcXIIoBX1+rDFi4JifIcNZg0sZOJJIzP41DB06FF9++WWsno6IiE7D0eIW3VareflCvLC/EVEk9Q4PHl9/GG2Bowd+fwAKmQT6zJMzzw0GA7RabeKKpD6nOz1ryZIlWLNmDV5//XVkZ2eH1mDU6XTQaDSw2+2YM2cOWltb8e9//xt2uz20/mJBQQFkMhnmzJmDESNG4LrrrsMf//hHWCwW3HXXXViyZAmDRaI0Yml2ora5JSxwnFmqxtiBnOFI4aTRPqC9ybR/2Ww2HDx4EHfddRcGDx4cjxqJiOgUXp8fzY5W0VhBbnaCqkkfsexvTz75JMaMGQOtVgutVoupU6fi3XffDR13u91YsmQJ8vLykJWVhUWLFoUuQyOi5Lf7RDN+8+JeNLd6Q4EjAIwvyYBS1vbndWFhIQNHiptY9yybzYaZM2eiqKgo9PXiiy8CAHbu3Ilt27Zh7969GDRokOg+lZWVAACZTIa33noLMpkMU6dOxQ9/+ENcf/31+P3vfx/z752IEqPB7sSaHVVhgeMkowrjBnGGI0UW9b+KnJycsEWLBUFAaWkp1q5dG7PCiIgosrqmlrAxgz4rAZWkl1j2t5KSEvzhD3/A4MGDIQgCXnjhBVx22WXYtWsXRo4cieXLl+Ptt9/GSy+9BJ1Oh6VLl2LhwoX4/PPPY/ktEVEcHK5twd/WH4YgtM1wbN+wo59eiXnDdZBIJDAajcjMzExwpZTOYtmzOgYIHc2cOfOM9wGAfv364Z133onqtYkoNbhcroiBoyFTjnOGlUIm4/ryFFnUoeMnn3wiui2VSlFQUIBBgwYx2SYi6gXWBofodlaGChq1MkHVpI9Y9rdLLrlEdPv+++/Hk08+ia1bt6KkpATPPvss1qxZgwsuuAAA8Nxzz2H48OHYunUrpkyZ0rNvhIjiKlLgmK2W4eqz9FDKpSgqKkJGRkaCq6R0x3MyIuotDfYWvL6nGt6AOHCUyWS44qx+fM+h04r6X8d5550XjzqIiKiLrA120W1DHi/fi4V49bdAIICXXnoJTqcTU6dOxY4dO+Dz+TB79uzQfYYNG4aysjJs2bKFoSNREvvT24fgcPng8bgRCARD4z+amo8stRwmkwkajSaBFVJfwXMyIuoNra2teHlXNVp84YHjpaNNyFJxXXk6vS6Fjm+88UaXn/DSSy/tdjFERHR6ew5V4emXPhWNGXJ5aXV3xbO/7d27F1OnToXb7UZWVhbWrVuHESNGYPfu3VAqlcjJyRHdv7CwMLR4fyQejwcejyd0u30RfyLqHZZmNw6a7XC73QgGTwaOt88sRH6WEiaTKWxHX6JY4jkZEfUmp9OJrd+aIwaOhTmZKM/jrH46sy6FjpdffnmXnkwikYQuMyEiotgRBAGvf7wH/35ja9ixkiJ9AipKD/Hsb0OHDsXu3bths9nw8ssv44YbbsDGjRu7UWWb1atXY9WqVd1+PBF136EaB/741gG43R5R4HjBkGwYtCqYTCbu0Etxx3MyIuotTqcTe46asbte/F4ik8lgzM3ClWOMYevKEkXSpdDx1D+uiIiodzldHjy5dhO27D4SdkylVGD2lGEJqCo9xLO/KZVKDBo0CAAwYcIEfPnll/jLX/6CH/zgB/B6vWhubhbNdqytrYXRaOz0+VauXIkVK1aEbtvtdpSWlsatfiIC7C4fnvnkKPZX276b4Sie7TF7WC6Ki4uhVHJdXYo/npMRUW9oaWnBjiNmbK8Tv+fI5XLoszNw1biiBFVGqYgrfhIRJbHDJ6x45IUPUdsQfilthlqJ2667AAX67Li9vt/vh8/n4xplMRAMBuHxeDBhwgQoFAp89NFHWLRoEQDg0KFDqKiowNSpUzt9vEql4kwqol721q4a7K+2weVyi3bsVMoluGN2MQNHIiJKKw6HA3uO1UQMHFVKJX4wtvMPyIki6Vbo6HQ6sXHjRlRUVMDr9YqO3XbbbTEpjIioLxMEAW9v3It/vrFVtFkBAEgALJo7AVfOOQtyuSxur2+329HQ0ACJRIKysjLIZPF5rWQSq/62cuVKzJ8/H2VlZXA4HFizZg02bNiA999/HzqdDosXL8aKFSug1+uh1WqxbNkyTJ06lZvIECWZPScaIwaOt0wzYuiAMigUXECfEofnZEQUS3a7HYcqa7HNGjlwvGp8EZRyaYKqo1QVdei4a9cuXHTRRWhtbYXT6YRer0d9fT0yMjJgMBjY4IiIYuCl93fgxXe3h423z26cNKp/3F7b5/PBarXC5XKFxurq6k576W86iGV/s1qtuP7661FTUwOdTocxY8bg/fffx4UXXggAePTRRyGVSrFo0SJ4PB7MnTsXTzzxRLy+NSLqBo/Hg9omhyhwHJCnwrVnGzBkQBnkcl4wRInDczIiiiWbzYaj1VZsqhGv4aiQy6FUKnHtBBOyVex7FL2oY+rly5fjkksuQVNTEzQaDbZu3YoTJ05gwoQJeOihh+JRIxFRnxIIBCMGjkP6F+LhX18Zt8BREATYbDZUVFSIAkegbW0Xp9MZl9dNFrHsb88++yyOHz8Oj8cDq9WKDz/8MBQ4AoBarcbjjz+OxsZGOJ1OvPrqq2kf6hKlErfbjWMnKuHxiWd7XDE+H0MH9mPgSAnHczIiipXm5mbU1dVhX5O45ykUCiiVSiwaY2TgSN0Wdei4e/du/OIXv4BUKoVMJoPH40FpaSn++Mc/4s4774xHjUREfUYgEMRf/v1x2Pi4YaW4d9mlMMRp/Uafzwez2Yy6ujrRrJ522dnZUKvVcXntZMH+RkQA4HK5YDab0ej0icalUilGDOrXJ5aaoOTHnkVEsdDU1IT6+nqccARhdZ08B1AoFFAqFLhkpAEFWVy7mLov6tBRoVBAKm17mMFgQEVFBQBAp9OhsrIyttUREfUhDqcbd//tTXy+87BoXCqV4o6b58Rl/cbTzW4E2tZwKSoqQmFhYdqfaLO/EVFrayvMZjOCwSD21px8T5TJpCjIyUKGims4UnJgzyKinhAEAY2NjWhoaIDVJWB3w8lZju2B4/mD8lCsS+9JBxR/Uc+RHT9+PL788ksMHjwY5513Hn73u9+hvr4e//rXvzBq1Kh41EhE1Cc8vmYDDhytEY0p5DKsvGU+1HE40Y20duOptFot8vLy0j5sbMf+RtS3OZ1OWCwWCIKAb6xubPjWAQCQyWRQqVTQZ3H3eEoe7FlE1F3tgWNTUxMEQcBXDSfXcVQqlVAoFBhlzMJQQ2YCq6R0EfVMxwceeABFRUUAgPvvvx+5ubm49dZbUVdXh6effjrmBRIRpTuH043H12zAl/uOi8bbA8exQ0ti+nqCIKC5ufm0sxtNJhMMBkOfCRwB9jeivqylpSUUODo9AfzrywYAJwNHiUQCI2d7UBJhzyKi7hAEAQ0NDWhqagIA2H2A0992rD1wLNdrcE7/nMQVSWkl6pmOEydODP2/wWDAe++9F9OCiIj6EofTjV899AqsjY6wY7/72cUYMbAopq/n9XphtVrhdrsjHtdqtcjPzw9dstWXsL8R9U0OhwO1tbWh2+8esAEA5PK2wBGQAADmjC5MRHlEEbFnEVG0BEFAfX09bDYbHF4BB5qDqGltW8exPXBUyqSYMyQPEokkwdVSuoj6rPK+++7DsWPH4lELEVGf89bGvREDx4vPGxPTwFEQBDQ1NaGysjJi4Hjq7Ma+GDgC7G9EfZHdbg8FjoIg4LMjDuypdkEul4sCx/+7bDj6F/AyM0oe7FlEFA1BEFBXVwebzYZvbUF8bA6EAkeVSgWFom0pp8EFGQwcKaaiPrN86aWXMGjQIJxzzjl44oknUF9fH4+6iIjSmiAIePOTr/DqBzvDjk0Y0Q/fnz8hZq/l9XpRXV2NhoaGiDtT63Q6lJWVISMjI2avmYrY34j6lubmZlitVgCANxDE63ub8f5B+3eBoxLtgeO155ShnIEjJRn2LCLqKkEQYLVaYbfb8a0tiP1NJzeNUalUkMtPXgA7sjArESVSGos6dNyzZw+++uorzJw5Ew899BBMJhMWLFiANWvWoLW1NR41EhGllb3fVOOOh17B869tRrBDCHjTFefgzp/MR6am5xsWdHV2Y0FBQZ+d3Xgq9jeivqOpqSkU0jjcAdz7Xg12VLZCoVCIAsf+BRk4f4QhgZUSRcaeRURdIQgCamtr4XA4cMR++sDx4hEF0GfEfvNK6tskQqRpL1H4/PPPsWbNGrz00ktwu92w2+2xqi3m7HY7dDodbDYbtFptosshoj5GEAT8bc0GbPjiUMTjM88eimXXnh+T1/J6vaitrYXH44l4XKfTIS8vL2nDxmR4v072/pYMPyOiVNP+YUxjYyNaPAFsPOzA1uNOAGhby0qpQHvgqJBJcNvcwRhu4u8X9Vy837OTvWd1BfsaUWwJggCLxYLqxhZ8ZgkgcEryo1apIPsucLxwcB766zWQSXlZNXVdV9+zo95IpqPMzExoNBoolUo4HOHrkhEREeD1+fH5ziOdBo4XnzcGN1w+pcev035C3dTUFPFSaoVCAYPBAI1G0+PXSnfsb0TppX3HzubmZgSCAv6+pR4N323ZqVQqoFAoQ/edP9aIi8cVQaWQJapcoqiwZxHRqYLBICwWC+rtTmyp7TxwvGlSMVTy5JyEQOmhW6HjsWPHsGbNGqxZswaHDh3Ceeedh1WrVuF73/terOsjIkpJgiBg8+6jOFpZh4+3HYLL7YXPH4h439uvm4XpEwf3+DU9Hg+sVmunsxtzcnKg1+uTdnZjMmB/I0pPp+7YCQBfVDhPCRyVoQX0AeCmGf0xbUh+QuokigZ7FhFFEgwGUVNTg9bWVnxpDcJ78opqqNVqyGRtH6jNG5rPwJHiLurQccqUKfjyyy8xZswY3HTTTbj66qtRXFwcj9qIiFLWf9/+Eq+sD98kpqP//HEx1KqerZ3C2Y2xwf5GlJ7aF9B3OBwQBAEffePAxsNtM8FUKiXk8pPvwTdM78fAkVICexYRRdIeODpbW7HNGkSz9+S5QXvgKJNKcM34ImQqOZuf4i/q0HHWrFn4xz/+gREjRsSjHiKilOZwurFzf0WXAse7frqgx4EjZzfGDvsbUfppX0C/paUFQUHAU5/VocbuAyAOHAcVZuHXFw+FRML1rCg1sGcRUUeBQAA1NTVwu9040CTA6moLHCUSCVQqFWQyGS4faUBhtpL9jnpN1KHj/fffH486iIhSXrOjFXf86RU02pynvV9RgQ4XnjMC44eXdvu1BEFAY2MjmpqaIh5XKpUwGAxQq9Xdfo2+hv2NKL20L6DvdLa9Jx9v8J4SOIp37Lz+3H48AaOUwp5FRKcKBAIwm83weDyocgZx2N52TfWpgeM4UzaMWlWCK6W+pscbyRARUZtte451GjguOG80zhk3EEPLC3t8YuvxeFBbWwuv1xvxeG5uLnJzczm7kYj6rPYF9FtbWwG0BZDvHbBBIsF3J18n/wT+5UVDYMrl8hNERJSaTg0cjzuC2NNwMnBUq9WQSqUoylZhnCk7wZVSX8TQkYgoRiz19ojjZ40ow80Lp/X4+Tm7kYjozNrXs3K5XKGxow1eWBw+qFQnF9AHgL9dPx5qrmlFREQpyu/3w2w2w+v1dho4DsrLwKzBes7op4Rg6EhEFCM1dbawsasXnI0rZo3r8XO73W5YrdbTzm7U6/nHBBH1baeuZ9WuwenHC1/UiwJHmVSCX188lIEjERGlLL/fj+rqavh8vk4DR61KjhkDcnmOQAnD0JGIKEa+3HdcdPvmhdOw4LzRPXrOYDAY2pk6EqVSicLCQqhUXJ+FiPq2Uy8vAwB/QMC7B2zYXtH63cnXyYBxzuhCDDBkJapUIiKiHvH5fDCbzfD5fNheF0C18+SmMe2BIwB8b2whlDIuuUSJ063Qsbm5Gc8++ywOHDgAABg5ciRuvvlm6HS6mBZHRJQK/P4A7vzza2HjhryerZvidrtRW1sLn88X8bher0duLj+5jCX2N6LUdOrlZQDQ7PLj4Y9rw06+AEAuleCcwXmJKpUoZtiziPomn8+H6upq+P1+HGgKhgJHqUQC1SkzHH8wzgiZlOcJlFhRR97bt2/HwIED8eijj6KxsRGNjY145JFHMHDgQOzcuTMeNRIRJbWPth7Ekcq6sPExQ4q79XzBYBD19fWoqqqKGDiqVCqUlpbycuoYY38jSk3tl5e1B44tnkCngaNaIcVPLhiAohxuHEOpjT2LqG/yer2hwPFbWxDf2NouqZZKJFBrNKGed/koAwNHSgpRz3Rcvnw5Lr30UjzzzDOQy9se7vf78aMf/Qi33347Nm3aFPMiiYiS2c79FWFj0ycMhkqpiPq5XC4XrFZrxLBRIpGEdqZm2Bh77G9EqefU2R4A4AsI+H+f10EikUCjUUMiORk4zhldiAtHFSI3U5mocolihj2LqO9pDxwDgQBqWoPY3/Rd4CiVQq1Wh84PFp9dDAUvqaYkEXXouH37dlFzAwC5XI5f/epXmDhxYkyLIyJKBbsOVopuK+Qy3HLl9KieIxgMorGxEc3NzRGPq1QqGAwGrt0YR+xvRKnF6/XCbDaHAkcA+OCgDXZPMCxwvGlGf0wbkp+IMonigj2LqG/xeDwwm80IBAJwBwTsqIscOP5ocgnknOFISSTq+Fur1aKiInxWT2VlJbKze7Z+GRFRqvl81xEEAkHR2OrlVyBD0/WZNC6XC5WVlREDR4lEgry8PJSUlDBwjDP2N6LU4fF4RDMcAeCTb+34osL13cnXyT9xvz+5hIEjpR32LKK+w+12h2Y4CoKAXfVBBARx4KiUSRk4UlKKOnT8wQ9+gMWLF+PFF19EZWUlKisrsXbtWvzoRz/C1VdfHY8aiYiS0pGKOjzy/HrRmFIhR3FhTpceHwwGUVdXh+rq6tOu3cjLqXsH+xtRajj15KtdIChg8/HWsMDxxzPLMWe0MRFlEsUVexZR3+ByuWA2mxEMtk1y+MYmwOoSwmY4Xj3eyMCRklLUl1c/9NBDkEgkuP7660OfLisUCtx66634wx/+EPMCiYiS0Z5DVfj9E2+FjV85dwKUijO/tba2tsJqtYpm6bSTSCTQ6/XIyclh2NiL2N+Ikp/L5UJNTU3o5KvdOwedkMpVovfMcf1ycPZAfW+XSNQr2LOI0l974CgIAlx+AXsbg6hpFSCTyaBStfU8mVSCq8YZoVHIEl0uUUQSQRCE7jywtbUVR44cAQAMHDgQGRkZMS0sHux2O3Q6HWw2G7RabaLLIaIUdfiEFb9+5NWw8bIiPR759ZWnDQqDwSAaGhpgs9kiHler1TAYDFAq+/ZGB4l8v06V/saeRn1Na2srampq0PFP16+tfrzxtUP03iuRAE/fPIEf3FDSiNd7dqr0rK5gXyM66dSeZ3YG8eV3azieGjgCwHkDczHckJXIUqmP6up7dtQzHdtlZGQgJycn9P9ERH2B2+OLGDgCwC9vnnPaE9wzzW7My8uDTqfjSXKCsb8RJR+n0wmLxRIWOP5npw0VtmDY++alZ5n4Xkp9AnsWUfo5tec1eYROA8dcjRzDCjITWSrRGUW9pqPf78dvf/tb6HQ69O/fH/3794dOp8Ndd90VcU0yIqJ08r/3tkccf/hX30OxISfisWAwCKvVGrbLaju1Wo3S0lJeTp1g7G9EyamlpSUscKyxebHqfUvEwLFQq8KCsUW9XSZRr2LPIkpPp/a8BreATTVt6xfLZDKoVeJlRC4daeC5AyW9qGc6Llu2DK+++ir++Mc/YurUqQCALVu24J577kFDQwOefPLJmBdJRJQM9n1bjdc/3iMakwC47+eXo39x5J1RObsxdbC/ESUfh8OB2tra0G1BEPDJtw58eqwVKpUKbe/CYr+9fASkXEyf0hx7FlH6ObXnuQMCPrO0BY5yuRwqpbJt7RAAFw7Ow8B8zmym1BD1mo46nQ5r167F/PnzRePvvPMOrr766k7XKUsGXCeEiHrizj+/hkPHLKKxe5ZcgtFDisPuGwgE0NDQALvdHvG5NBoNDAYDFApFXGpNdYl4v061/saeRunObrfDarWGbguCgH9srUeVPQiVSolIgePD14yFLoPvq5R8Yv2enWo9qyvY16gvOzVwDAoC3jwRHjhmKWX4wTgjFLKoL1glirm4remoUqnQv3//sPHy8vI+v/EBEaW3Znur6HaGWhkxcHQ6nairq+t0dmN+fj60Wi1nNyYZ9jei5NHc3Iz6+nrR2J83WmH3oNPA8ambzoKcJ2LUR7BnEaWPUz9ka/ULWF8VeYbjFaMLGThSyon6X+zSpUtx7733wuPxhMY8Hg/uv/9+LF26NKbFERElE7dXvEbS4kXTRLcDgQBqa2tRU1MTMXDUaDQoKyvj5dRJiv2NKDk0NTWFBY5rdzbC4ZVEDBx/OmsAnlk8gYEj9SnsWUTpwWazhQLHevfJwFHRIXCcUKJFplKWsDqJuivqmY67du3CRx99hJKSEowdOxYAsGfPHni9XsyaNQsLFy4M3ffVVyPv8EpElGpOmBtgc7hEY4a8k9PInU4nrFYrAoFA2GM5uzE1sL8RJZYgCGhsbERTU5NovKnVj2/q/VAqFTg1cJRI2i6n1mp4OTX1PbHsWatXr8arr76KgwcPQqPR4JxzzsGDDz6IoUOHhu7jdrvxi1/8AmvXroXH48HcuXPxxBNPoLCwMHSfiooK3Hrrrfjkk0+QlZWFG264AatXr4ZcHvUpJ1GfcOqsfpdfwOffreGoUCigVChCgSMATCzhkgOUmqLuADk5OVi0aJForLS0NGYFERElG7O1GXf95XXRmFQiQakxF4FAAPX19XA4HBEfy7UbUwf7G1HiCIKAhoYGNDc3i8Yd7gD+9nlTxMtFn7yRl1NT3xXLnrVx40YsWbIEkyZNgt/vx5133ok5c+Zg//79yMzMBAAsX74cb7/9Nl566SXodDosXboUCxcuxOeffw6g7WqPBQsWwGg0YvPmzaipqcH1118PhUKBBx54oGffLFEaampqQkNDAwRBQKVTwK76IIDwwPG8AbkYXpiVyFKJeiTqjWRSGRcnJqLu+Ot/PsGGLw6JxqadNQi3LJqCurq6iLMbpVIp8vPzkZ2dzdmN3cD36zPjz4jShSAIqK+vF218YXcH8O5+G75pCIR9aJOTocDqH4zmulaUUlLpPbuurg4GgwEbN27EjBkzYLPZUFBQgDVr1uB73/seAODgwYMYPnw4tmzZgilTpuDdd9/FxRdfDLPZHJr9+NRTT+HXv/416urqurTOZCr9jIi669RZ/ccdQexvCsLXlje2BY6n/K6cNzAXww0MHCk5dfU9O+q/1g4ePNjpsffffz/apyMiSmonzA1hgaMgCFhwzkBYLJaIgWNGRgbKysp4OXWKYX8j6n2CIMBqtYoCR5cviD99ZMG3jeGBIwCsmD+EgSP1efHsWe2/j3q9HgCwY8cO+Hw+zJ49O3SfYcOGoaysDFu2bAEAbNmyBaNHjxZdbj137lzY7XZ8/fXXPaqHKF2cGjh+1RDAnoaTgaNSqRQFjucP1DNwpLQQ9V9sZ511Fh5//HHRmMfjwdKlS3HZZZfFrDAiomSw8tHXRLf9fj9uvHgcZJLIsxsNBgOKioq4flEKYn8j6l2CIKC2tla0PEWD048/rK+BSqWCXC4OHDNUMvzkggEw5Wp6u1SipBOvnhUMBnH77bdj2rRpGDVqFADAYrFAqVQiJydHdN/CwkJYLJbQfU4NHNuPtx+LxOPxwG63i76I0lX7MiJNTU2oaAnimOPkBadKpVL0IduEEi2GFGQkokyimIv6rPj555/HrbfeirfffhvPPfccampqcM011yAYDOLTTz+NR41ERAnx5b7j8Hy3Y7UgCPB4vAgGAhhenh9234yMDBgMBoaNKYz9jaj3CIIAi8UCp9MZGvP4g/jzhtrvAkfxe+n4/jn4/uRSFGSrertUoqQUr561ZMkS7Nu3D5999lkMq41s9erVWLVqVdxfhyjRTl1GRBAEfNUQDB07NXAcaczC5FIdlHLO5qf0EfW/5u9///vYs2cPfD4fRo4cialTp+K8887Dzp07MWnSpHjUSETU6xqaW/CHZ96DILTNbmxtdSEQ8OOnV04WXTItlUpRWFjI2Y1pgP2NqHcEg0HU1NSIAkcAWLuzCWp1eOC4+LxyLJk9iIEj0Sni0bOWLl2Kt956C5988glKSkpC40ajEV6vN2yjp9raWhiNxtB9amtrw463H4tk5cqVsNlsoa/Kyspu1U2UzARBQF1dXWjZgkPNAgLfTXJUqVShwPFHk0swvTyXgSOlnW7/i/Z6vQgEAggEAigqKoJarY5lXWHuueceSCQS0dewYcPi+ppE1De9/vEe3HL3vxEMCvB43PB4PAAETBpZipEDT146lJmZibKyMm4Wk2Z6u78R9SXtgWNra6to/LOjLahyADKZOHBcMnsgpg7O680SiVJKLHqWIAhYunQp1q1bh48//hjl5eWi4xMmTIBCocBHH30UGjt06BAqKiowdepUAMDUqVOxd+9eWK3W0H3Wr18PrVaLESNGRHxdlUoFrVYr+iJKJ+3rFrcvHXDEHsQhW9ssx1Nn9f94cgnkUp5LUHqKOnRcu3YtRo8eDZ1Oh2+++QZvv/02nn76aUyfPh1Hjx6NR40hI0eORE1NTeirN6b9E1HfYbY24//+8hpeeG0L/H4/XC5XaKMYvTYD1140DsDJ2Y1Go5GzG9NIIvsbUV8QCARgNpvhcrlE45XNPmw85oFMJhONL5xUjPH9c3uzRKKUEcuetWTJEvz73//GmjVrkJ2dDYvFAovFEvpd1el0WLx4MVasWIFPPvkEO3bswE033YSpU6diypQpAIA5c+ZgxIgRuO6667Bnzx68//77uOuuu7BkyRKoVJylTH3PqesWBwUBXzcFsa8xPHAcXpgJGQNHSmNRh46LFy/GAw88gDfeeAMFBQW48MILsXfvXhQXF2PcuHFxKPEkuVwOo9EY+srPD19XjYioOz7beRi33b8W+w/XiGY3tvvxwkmQy6Sc3ZjGEtnfiNJde+DodrtF4xaHH//aaQ8LHAHgorFFvVUeUcqJZc968sknYbPZMHPmTBQVFYW+XnzxxdB9Hn30UVx88cVYtGgRZsyYAaPRiFdffTV0XCaT4a233oJMJsPUqVPxwx/+ENdffz1+//vfx+pbJkoZ7esWVzc68PpxP948EcDh72Y4qk8JHKUSYEY5P1yj9Bb1FJ2dO3di6NChorHc3Fz873//w7/+9a+YFRbJt99+C5PJBLVajalTp2L16tUoKyvr9P4ej+e74KANd0QjokgEQcDfX/4MXp8fXq8Xp4aNAHDTZRPRvzgPBQUFyMrKSkyRFHeJ7G9E6czv98NsNn/3/tpGEAQ8tbkeTR4ZpNLwwPGehZEvxySiNrHsWYIgnPE+arUajz/+eNiO2afq168f3nnnnahemyjdBINBVFTXYH+tEweag6JjarVa9CHbD88ycRIDpb2oQ8ehQ4fC7/djw4YNOHLkCK655hpkZ2fDbDbjiiuuiEeNAIDJkyfj+eefx9ChQ1FTU4NVq1Zh+vTp2LdvH7KzsyM+hjuiEVFX7D9iRl1Dc+hS6nYjBxbixwvPRo5Oi4KCgogzcSh9JKq/EaUzn88Hs9kMn88nGn/3oOO7wDH8opvb5g5CiT6jt0okSknsWUTJx+sP4JUdx2F2+MKOdQwcr59gQoaS5xaU/qIOHU+cOIF58+ahoqICHo8HF154IbKzs/Hggw/C4/HgqaeeikedmD9/fuj/x4wZg8mTJ6Nfv3743//+h8WLF0d8zMqVK7FixYrQbbvdjtLS0rjUR0SpRxAEOBwOvPre1rDAccV10zG4rICzG/uQRPU3onTl8/lQXV0Nv98vGrd7gT0Wf8TAccG4IowpzemlColSF3sWUXI51uDEa3uqEQyKZzdKJBKoVCrIZDIoZVIMLcjA2WU6KGTcpZr6hqj/pf/85z/HxIkT0dTUBI1GExq/4oorRDuaxVtOTg6GDBmCw4cPd3of7ohGRJ3x+XyoqamB1WrFsepG0bHRg40YM7QMZWVlDBz7kGTpb0TpwOv1oqqqKixwbPYAj3/eCIkk/E/Q310xAldMLO6tEolSGnsWUfL4ymzDG1+ZTxs4zhqsx81nF2NaeS4DR+pTop7p+Omnn2Lz5s1QKpWi8f79+6O6ujpmhZ1JS0sLjhw5guuuu67XXpOIUp8gCLDb7WhoaEAwGEQwKKCuyRk6LpFI8L25Z8NoNCawSkqEZOlvRKnO4/HAbDaHzSBXKBR48pPaiIHjM4sncF0roiiwZxElliAIONLgwq5qG6oaHBEDR7VajbNKdJhQomXQSH1W1KFjMBgM+yMSAKqqqjpdWzEWfvnLX+KSSy5Bv379YDabcffdd0Mmk+Hqq6+O22sSUXrx+XywWq1wuVxtt/0BvPPZIfj8be9pcrkcSqUSQwdypk1flKj+RpRO3G43zObw2R4qlQrPbbdHDBx/PncwA0eiKLFnESWOxx/Ec19WQxAEuN3uiIHj2f3zcM6APEjZ36iPizpunzNnDv785z+HbkskErS0tODuu+/GRRddFMvaRKqqqnD11Vdj6NCh+P73v4+8vDxs3boVBQUFcXtNIkoPgiDAZrOhoqIiFDjaHG7c89SHWL/12+8ufVBDpVKhQJ8NXZbmDM9I6ShR/Y0oXbhcroiBo0Kpwitft6KiwRX2mLljCjG6VNdbJRKlDfYsosTYXmU7beCokErwk3P64dyB+QwcidCNmY4PP/ww5s6dixEjRsDtduOaa67Bt99+i/z8fPz3v/+NR40AgLVr18btuYkofXWc3djug63fwtbiDs1ubJ9lM3/6KM646aMS1d+I0kFraytqamogCIJoXKPR4JtmOfZV1YY9ZmSJFt+bVNJbJRKlFfYsot73TZ0T2yvtbYGjy4Vgh543Mk+O84aXQaNWdvIMRH1P1KFjSUkJ9uzZgxdffBF79uxBS0sLFi9ejGuvvVa0iDERUSK1z25saGgIOwl2urzYtPMYVCo15HJZaPzs0f1x8Xmje7tUShLsb0Td43Q6YbFYwt5rMzIyYDAU4oEP94Q9RpehwJLZg/ghD1E3sWcR9a6vzA5sPtGMYDAIt9sd1vMuKVehvKwECoUiQRUSJSeJ0PG3JY3Z7XbodDrYbDbuZE2UxrxeL6xWK9xud9ixBlsr/vTCZwhCIjrZnTNtBG65cjpPgJME36/PjD8jSgYtLS2wWCxh45mZmTAajXh7dw1e22EWHRtVosXt84b0VolESYHv2WfGnxElqwanFy99VRsxcJxUIEWZTomSkhLI5VHP6SJKWV19z+ZvBRGljdPNbgQAiUSK1c99CplMho7R4s1XTGPgSEQUBYfDgdra8Mums7KyUFhYiI/3W8MCRwC4bc7g3iiPiIioxzz+YKeB4wXFMuRlqmAymRg4EnWCvxlElBZON7sRALRaLX7/9EeQyWRhx669eDIUivBxIiKKzGazoa6uLmw8OzsbBoMBu080479bKsOOnzM4D1IpP+AhIqLkJwgCXv/aGjFwXFAmQ4ZaheLi4ojnF0TUhqEjEaU0QRDQ3NyMxsbGiLMb5XI5cnL1WPy7NREff+9tl2HEwKJ4l0lElDaam5tRX18fNq7T6ZCRnYPHPjiMvZW2iI+9cjI3jiEiotRwosmN+hZPWOB4vkmGTI0aJpOJgSPRGUi7cqfHHnssNHuooqIi4ok9EVFv83q9qK6u7vRyap1Oh9LSUvzsvpciPn7BeaMZOPZx7G9E0WlsbIwYOObk5KDBp8K9rx+IGDhmqmT441VjkK3mAvtE3cWeRdR7AkEBb++vDQsczzXKYNBqGDgSdVGXQscVK1bAbrcDAMrLyyNeTkNE1FsEQUBTUxMqKysjXk6tUChQXFwMuwv4/opn4PH6wu4jlUhw0xXn9Ea5lMTY34i6RhAENDQ0oLGxMeyYVJ2N/+5swkPvfIN6hzfseHGuBvd+bxT0WcreKJUobbFnEfWeTw/XwePxiALHQo0ExTkMHImi0aXLq00mE1555RVcdNFFEAQBVVVVna6bVlZWFtMCiYhO5fF4YLVa4fF4Ih7X6XTIy8vDH555Hzv2n+j0ef770I+4cQzFrb+tXr0ar776Kg4ePAiNRoNzzjkHDz74IIYOHRq6j9vtxi9+8QusXbsWHo8Hc+fOxRNPPIHCwsIef19EsdQeODY3N4cdO9QswztfV8PjC0Z8bLZajv+7bDiU8i59zk1Ep8FzMqLecaS2GTsqxB+ySQBMLs6AyWSCVMqeRtRVEqEL8/KffvppLFu2DH6/v9P7CIIAiUSCQCAQ0wJjqatbehNR8mmf3djU1BTxciKFQgGDwQBrUytWPBj5cmoAuPT8sbjh8qnxLJVioLfer+PV3+bNm4errroKkyZNgt/vx5133ol9+/Zh//79yMzMBADceuutePvtt/H8889Dp9Nh6dKlkEql+Pzzz7v0Guxp1BsEQUBdXV1odtWpTjgV+O+Xnc+0WjixGLNGGqDiRl1EMXnPTpdzss6wr1EycDqdeCrCRmiz+mdizIBiBo5E3+nqe3aXQkcAcDgcOHHiBMaMGYMPP/wQeXl5Ee83duzY7lXcC9jIiFLTmWY3ZmVn43CVHV99U42Pth7s9Hl+dvV5mDVleLzKpBjqzffr3uhvdXV1MBgM2LhxI2bMmAGbzYaCggKsWbMG3/ve9wAABw8exPDhw7FlyxZMmTLljM/JnkbxJggCrFYrHA5H2DG7kIlnPjPDFxD/GamQSXDOkHxcPsHE9RuJThGr9+x0OCfrDPsaJZrT6cS2b83YVS8O7XM0Ctx8zgBeJUV0iq6+Z3d59+rs7GyMGjUKzz33HKZNmwaVShWTQomIOtM+uzHSGmJA2+zGgESNpQ+sw5k+PfnXH25GhobriVG43uhvNlvbxhp6vR4AsGPHDvh8PsyePTt0n2HDhqGsrKzT0NHj8YiC90gzz4hiRRAE1NbWoqWlJexYVk4e/vru8bDAsUSvwS8uGsKwkSiOeE5GFB8tLS04Vm0JCxzlcjmuGFfKwJGom7ocOra74YYbALSdMB04cAAAMGLECJx11lmxrYyI+jSPx4Pa2lp4veGbEgBtO6V6AjKseODF0z7POeMHYuk1M6FS8iSYTi9e/S0YDOL222/HtGnTMGrUKACAxWKBUqlETk6O6L6FhYWwWCwRn2f16tVYtWpVj2oh6opgMIja2lo4nU7RuEQigcFgwF2vHYbTIz4pG1umw89mD4JMypMyot7AczKi2HE4HPj0UA0ONIvXJ5bL5SjWZ0GfyYkLRN0VdehotVpx1VVXYcOGDaGTpebmZpx//vlYu3YtCgoKYl0jEfUhgiCgsbERTU1NEY8rlUoYDAY0t3hx2wNrOn2eXG0GHlh+BQz67HiVSmkmXv1tyZIl2LdvHz777LMe1bdy5UqsWLEidNtut6O0tLRHz0nUUTAYRE1NDVwul2hcIpHAaDTil/87GDbDsSBbhZ9cMJCBI1Ev4jkZUWw022x4c58FVpe4t8nlcuRkaXDJCEOCKiNKD1Gvgrps2TI4HA58/fXXaGxsRGNjI/bt2we73Y7bbrstHjUSUR/hdrtRWVnZaeCYm5uL0tJSyGQKLLm388Dxe3POwl/u/AEDR4pKPPrb0qVL8dZbb+GTTz5BSUlJaNxoNMLr9YbtBlxbWwuj0RjxuVQqFbRareiLKJaCwSDMZnPEwFGXZ8Ddrx8OCxwBYOmcQdydmqiX8ZyMqOesDU14Y2/kwFGlVGLB8AKo2N+IeiTqmY7vvfcePvzwQwwffnIzhhEjRuDxxx/HnDlzYlocEfUNXZ3dqFar4fb4cMefXo54P24UQz0Ry/4mCAKWLVuGdevWYcOGDSgvLxcdnzBhAhQKBT766CMsWrQIAHDo0CFUVFRg6lTurk69LxAIwGw2h23YJZVKkZGTj4feP4bmVl/Y4344rQzFuZreKpOIvsNzMqKeqa1vxH92W8PWhVfI5VAqlZg/vAD5vKyaqMeiDh2DwSAUivC10RQKBYLBYIRHEBF1zu12w2q1drp2Y25uLvR6fWjx5tseWIuGZmfY/a69eDIDR+qRWPa3JUuWYM2aNXj99deRnZ0dWqdRp9NBo9FAp9Nh8eLFWLFiBfR6PbRaLZYtW4apU6d2aedqolgKBAKorq4Oex+WSqXQ6g34zcsHIz4uQyXDzOG87IwoEXhORtQ9Hn8QWw5bsKMqfEM+hUIBpUKBm88u4Qx+ohiJ+jfpggsuwM9//nOYzebQWHV1NZYvX45Zs2bFtDgiSl/BYBD19fWoqqqKGDgqlUqUlpYiLy8PEokEgUAQf/3PJxEDxxU3XoiFF47vjbIpjcWyvz355JOw2WyYOXMmioqKQl8vvnhy46NHH30UF198MRYtWoQZM2bAaDTi1Vdfjdn3Q9QVfr8/YuAIiRTHW9WdBo4yqQR/vnZc/Askooh4TkYUvf21Lfh/nx/rNHA8u38eFk9m4EgUSxJBEMIX5zmNyspKXHrppfj6669DC9hXVlZi1KhReOONN0RrViUbu90OnU4Hm83GtbCIEsjtdqO2thY+X/ilegCg1+uRm5sbmt3Y7GjF3X99E1W14Zdf/2rxXEweUx42TqktEe/Xqdbf2NOop3w+H8xmc9h7sUQqw/0f1kEqjXzS9bPZAzG+X07oPZqIzizW79mp1rO6gn2N4umgtQUfHIh8/qFQKDBvhBFDCjITUBlRaurqe3bUl1eXlpZi586d+PDDD3HwYNun38OHD8fs2bO7Xy0R9QnBYBCNjY1hm2e0U6lUMBgMUKlUANrWxXtn0z7849XPI97fmK9l4Egxw/5GfYnP50N1dTX8fr9oXCo7feD4w2llOKt/bm+USESnwZ5F1HX+QBAbvrFGDByVSiXmjzBiUH5GAiojSn9Rz3RMZfz0jChxXC4XrNbIzV4ikSA3N1c0u1EQBDz14iZ8uOVAxOfLy8nEE7+9BnK5LK51U2Lw/frM+DOi7vJ6vaiurkYgEBCNy+Ry3LfeCokkPHDMVsuxbM4gDDBk9VaZRGmF79lnxp8RxYMgCFi/rwp7a8OXaDq7LAejS/OQowlfH5WITi9uMx2JiKIRDAbR0NAAm80W8Xik2Y2fbDuEV9bvhKU+fL0VgLtUExF1l8fjgdlsDgscFQoFfv9BbaeB4/1XjkKGin82EhFR6hAEAdUWa8TA8dpxhTDmc+Y+Ubzxr0ciipszzW7U6/XIyWlbF6y+qQX/enMrvjpUDXuLK+LzSaVS/Oyq83D+5KHxLp2IKO243W6YzeawnW2VSiX+8mljxMBxxtB8XD+9fy9VSEREFBuCIMBSW4v/fd0cdmzOkDwGjkS9hKEjEcXcmWY3qtVqGAwGKJVKAMD7n32Np1/69LTPOaC0AKtvv5yXUxMRdYPL5YLZbEbHVXVaAzKsfr824qYw4/vnMHAkIqKUIwgCDhw3490jjrBjZXlZGF1WkICqiPomho5EFFOtra2wWq1hmxMA4bMbAeC9T7/GMy+fPnC8aMYo/PCSyQwciYi6obW1FTU1NWGBo0Kpxl/er4kYOBbqVFgye1BvlUhERBQTgiBgz5FqfHS8JeyYSqXC+FJ9Aqoi6ru6HTparVZYrdawS3TGjBnT46KIKPUEg0HU19fDbo+8DmPH2Y1HK+vw4LPvo74p/A8CAFApFZg9dRh+MH8iMjWquNVN1BH7G6UTp9MJi8USFjhqNBr84aPIMxzPH1GAa8/p11slElEPsGcRnRQMBvHazhM41uwJO6ZWqXB2fz13qSbqZVGHjjt27MANN9yAAwcOhP6AlUgkEAQBEokkbGFyIkp/Z5rdmJeXB51OB4lEApfbi9/97U0crazr9Pnu+ukCjB9eGs+SicKwv1G6aWlpgcViCRvPzMzEa1874fIGw46dOySfgSNRCmDPIhJzuH1Yt6sCdc7wteTVajVmDMzDKGNWAioj6tuiDh1vvvlmDBkyBM8++ywKCwsjfkJORH1DIBBAQ0PDaWc3FhYWQqFQAABOmBuw4sGXOn0+hVyGv911NfJz+QcB9T72N0ondrsdVqs1bDwjMxPPf9mMI9bwnTxvOX8Azh7Iy86IUgF7FlEbbyCI1/bWwtzUEjFsz8zQ4OIRhSjJUSegOiKKOnQ8evQoXnnlFQwaxHV+iPoyp9OJurq6Ls1u3HOoCk/+dyPqmsIXc243f/ooXHXRJGRl8FJqSgz2N0oXNpsNdXXhs8mbfEr84e0qAOHhxJVnlzBwJEoh7FlEwD6LA58ebYLb7Q5bYkAikUClUuHqs0zQqRUJqpCIog4dZ82ahT179rDBEfVRgUAA9fX1cDgiB4gajQYGgyE0u/FMO1Mb87VYtfRSzm6khGN/o3TQ3NyM+vr6sPETDin+u6MWkQJHg1aFOaMLe6E6IooV9izq6zYfb8Ies6PTwHGkKQcXDCmAQiZNUIVEBHQjdPz73/+OG264Afv27cOoUaNCwUK7Sy+9NGbFEVFycTqdsFqtES9dkEgkyM/Ph1arDV3i0+ry4plOAkcJgB99bzouPGc4ZPxjgJIA+xulusbGRjQ2NorGTjR68GW1H4cbvIgUOGaqZPjt5SN4aSZRimHPor5sb42j08AxSyHBpWOLUZTDCQ1EySDq0HHLli34/PPP8e6774Yd46LFROkp2tmN7Z5YuxFChPtPGVOO78+fhH4mXspHyYP9jVKVIAhobGxEU1NTaMwfEPD6vmbst/q+e28ODxUXTirGRWOLerFSIooV9izqq2odHnx2LPIl1VOMCkwcXAKViss1ESWLqKcXLVu2DD/84Q9RU1ODYDAo+mJzI0o/TqcTFRUVEQNHqVSKgoICmEwmUeDo8frw9P8+xZbdR8Ie85c7f4A7Fs9l4EhJh/2NUpEgCKivrxcFjgDw4Td27Lf6oVAoESlwvP/KUQwciVIYexb1RYIg4NW9tXC7XKLAUSoBLh+gxKQhpQwciZJM1DMdGxoasHz5chQWcu0fonQWCARQV1eHlpaWiMczMjJQUFAgChsDgSBe/3gP/vPWtoiPuf/nl6OkMDcu9RL1FPsbpRpBEFBXVwe73S4aP1LvxvZqb9jscwAYbsrG9dP7oyCbJ2VEqYw9i/qaFo8f/9phbgschZPXUmUrJJjTT4Xi4uKIfY+IEivq0HHhwoX45JNPMHDgwHjUQ0RJoKWlBXV1dRE/KZdKpcjPz0d2drZoDTCH040f/+5f8Pkjf7p+weRhGDbAGLeaiXqK/Y1SiSAIsFqtYbPQa+w+/He3A3K5+MRrdKkO15/bD7mZyt4sk4jihD2L+pJAUMCbX9fC5XJBEMSLN51tVDJwJEpiUYeOQ4YMwcqVK/HZZ59h9OjRYb/ct912W8yKI6Le1ZXZjQaDAXL5ybeOmjobXl2/Cx9vO9jp8047axB+dvV5Ma+XKJbY3yhVCIIAi8UCp9MZNv7RUW9Y4Di+fw6WzOYOt0TphD2L+pJPj9SjpqklLHAcpldg1MBS0bkJESUXidDxN/cMysvLO38yiQRHjx7tcVHxYrfbodPpYLPZoNVqE10OUdIQBAFOpzOq2Y11jQ48v24ztn51rNPnNRXo8IOLJmHa+IHcGZWikoj361Trb+xpfVMwGITFYkFra6toXCKR4LOqID791iYaL8vLwJ2XDoNcFvUy3kQUQ7F+z45lz9q0aRP+9Kc/YceOHaipqcG6detw+eWXh463tLTgN7/5DV577TU0NDSgvLwct912G37605+G7uN2u/GLX/wCa9euhcfjwdy5c/HEE09Edfk3+xp15PEH8d4BK45YbWGB4/A8BS4cVcYZjkQJ0tX37Kg/Ejh2rPOAgYhSj9/vR11dXdiMmXaZmZkoKCgIfYLo9wfw2H8+wec7D5/2ea+7dAouu2Asw0ZKGexvlOyCwSBqamrgcrlE4xKJBFvMCAscAWDphYMYOBKloVj2LKfTibFjx+Lmm2/GwoULw46vWLECH3/8Mf7973+jf//++OCDD/Czn/0MJpMJl156KQBg+fLlePvtt/HSSy9Bp9Nh6dKlWLhwIT7//POY1Ul9i9nuxmt7a+F2u8MCx2nFKkwaUgaZTJag6oioqzgPmaiPEgQhtHbjqbu/tWvfmTorKwsSiQTHqurxj1c/x/4jNad9XlOBDrdddwEG9+PC5kREsRIMBmE2m+F2u0XjAoAt1cDGb5rCHjNrpAH6LK7hSESnN3/+fMyfP7/T45s3b8YNN9yAmTNnAgBuueUW/L//9//wxRdf4NJLL4XNZsOzzz6LNWvW4IILLgAAPPfccxg+fDi2bt2KKVOm9Ma3QWmk1RvAu/utEQNHY5YcEweXMnAkShFRh44333zzaY//4x//6HYxRNQ7ujq7EZBg5/4KfLnvONZvPnDG5739ulmYPnFwjKsl6h3sb5SsAoEAzGYzPB5PaMwXELCryoU91iAanP6wx+RmKnDl2SW9WSYR9aLe7FnnnHMO3njjDdx8880wmUzYsGEDvvnmGzz66KMAgB07dsDn82H27NmhxwwbNgxlZWXYsmVLp6Gjx+MRva/Z7faY1Uyp7ZWvamBzhm8aM0SvxKyRXMORKJVE/dva1CT+JN3n82Hfvn1obm4OfbJFRMkpmtmNH3y+H0+/9GmXnveWK6fj/MlDoVTwDwBKXexvlIwCgQCqq6vh9XpDY8caPHhuWz3Uag2k0siXTt99xUheVk2UxnqzZ/31r3/FLbfcgpKSEsjlckilUjzzzDOYMWMGAMBisUCpVCInJ0f0uMLCQlgslk6fd/Xq1Vi1alVMa6XU962lGdbm8E0tJxapMX14Wad9j4iSU9QJwbp168LGgsEgbr31VgwcODAmRRFR7Pn9flit1rDNB9plZWWhoKAA/kAQT724CR9uOfPMxh/Mn4jLLhgLlZILOFPqY3+jZOP3+1FdXQ2fzwegbXbjG/uasafaddrA8fEbxkOl4GVnROmsN3vWX//6V2zduhVvvPEG+vXrh02bNmHJkiUwmUyi2Y3RWrlyJVasWBG6bbfbUVpaGouSKUXZW5x4Z39t2PgF/TIwdmAJA0eiFBSTaUlSqRQrVqzAzJkz8atf/SoWT0lEMSIIAhwOB+rr6yPObpTJZCgoKEBmZiZeeG0L3tzw1Rmf87YfXoBzzxoEGWfRUJpjf6NE8fl8MJvN8Pl8EAQBFrsPT3xWB4lEArVaHXbiZcxRY2J5Li4eV8QZjkR9VDx6lsvlwp133ol169ZhwYIFAIAxY8Zg9+7deOihhzB79mwYjUZ4vV40NzeLZjvW1tbCaDR2+twqlQoqlSomdVLqczqd2PqtGf6g+JJqrVrOwJEohcXsWsgjR47A7w9fU4iIEqersxstDQ7c8H//77TPNXpIMS49fyzGDy/ljtTUp7C/UW/zer0wm83w+/3YfKwF7+5v25VaIpFAo1FDIhGfeF02wYSLxxXxvZmIYt6zfD4ffD5fWOAjk8lCH2ZPmDABCoUCH330ERYtWgQAOHToECoqKjB16tSY1ULpy+l04nhVDfY2BETjMpkMN0wpZ+BIlMKiDh1PnQIPtM2iqqmpwdtvv40bbrghZoURUfd1dXajxw+sfPQ1HKmsi/g8EgBzzx2Jy2eNQ4E+O85VEyUW+xslA6/Xi+rqagQCAXx4yI6Nhx0AAKm0bYZjx8Dx94tGwpSrSUSpRJRAsexZLS0tOHz4cOj2sWPHsHv3buj1epSVleG8887DHXfcAY1Gg379+mHjxo345z//iUceeQQAoNPpsHjxYqxYsQJ6vR5arRbLli3D1KlTuXM1nZY/KOCrinocqmmE2Sme4SiXyzF9UAGUci4XQpTKog4dd+3aJbrdvvHEww8/fMZd1Igo/nw+H6xWK1wuV8Tj2dnZyM/Px5Y9x/DoCx+e9rnuXnIJRg8pjkeZREmH/Y0SzePx4HhFFax2D9Z91Ywae9tajlKpFGq1ShQ4zh5pwA+mcOY5UV8Vy561fft2nH/++aHb7YHmDTfcgOeffx5r167FypUrce2116KxsRH9+vXD/fffj5/+9Kehxzz66KOQSqVYtGgRPB4P5s6diyeeeKIH3yGlu8ZWH9bsqBLtYN5OLpcjQ63CMENWAiojoliSCB33oU9jdrsdOp0ONpsNWq020eUQxZQgCLDb7aivr0ekX2uZTIb8/Hx8/OVR/PftL+DzByI8SxtTgQ4PLL8C2ZnqeJZM1Cm+X58Zf0bpxe124/3th/HqnkZ4/Sffw9sCR3UoXBxUmIV5Y4wY1y8nQZUSUXfwPfvM+DPqO5pdPvx7e+eBo0atwgWD8jAoPyMB1RFRV3T1PTvqmY4ulwuCICAjo+0N4MSJE1i3bh1GjBiBOXPmdL9iIuq2rsxu1GRm48b/++cZn+upu6/lpdTUJ7G/UaK4XC78d+NBrD9kF43LZFKoVCcDx4evGQtdhiIRJRJRkmHPolS27WhdxMBRIZdDn52By0cZkKWK2fYTRJRAUf8mX3bZZVi4cCF++tOform5GWeffTaUSiXq6+vxyCOP4NZbb41HnUQUwZlmN8rlcsiUGXj2tR3Ysf/EaZ/rdz+7GGOHlsSrVKKkx/5GidDS4sRznxzE5qMtonGZTAaVSgWJRILpQ/OxYFwRA0ciCmHPolTV3NyMfTX2sHFdhgrnDzGgNEcDpZwbxxCli6h/m3fu3Inp06cDAF5++WUYjUacOHEC//znP/HYY4/FvEAiiszn88FsNqOuri5i4BiEAu9vO4HbH3z1tIFjrjYD/7jvBgaO1Oexv1FvczqdeGXLt50GjkOLsnH7vMG4YXp/5GerElQlESUj9ixKRbX1jfjvbkvY+Dn9tFg8tT8G5mcycCRKM1HPdGxtbUV2dtullx988AEWLlwIqVSKKVOm4MSJ08+kIqKeEwQBNpsNDQ0NorDR6/PjRE0zDhyrw4HjjWi0R77Uut2MiYPxk+/PgFrFmTNEAPsb9S673Y63vjyG9/bbRONyeVvg+MerxkKfpUxQdUSU7NizKJUIgoDPv6nBtsrwGY4qpRKTBhi5MRpRmoo6dBw0aBBee+01XHHFFXj//fexfPlyAIDVauWCv0Rx5vV6YbVa4Xa7Q2M2hxtvf3YQX35dBQESKJXKMzbtlbfMx8SR/eJdLlFKYX+j3mK32/HvTd/i0yPiGY5yuRwqlRIPXT0WOZkMHImoc+xZlCoEQcCH+6vxVU1L2DGlUomxJbmQyzi7kShdRR06/u53v8M111yD5cuXY9asWZg6dSqAtk/Yxo8fH/MCiaitWTc3N6OxsRGCIEAQBBw8Xod3PzuEo9WNkEgkUKlUkMlknT7HlLEDMGfaCIwZUsxPEokiYH+j3mCz2fDZvsqIgWNWhhoPXzMWGVw8n4jOgD2LUoEgCNh4sPPAcWihFtPKc3q/MCLqNRIh0mJwZ2CxWFBTU4OxY8dCKm37VOKLL76AVqvFsGHDYl5krHR1S2+iZHLq7EZBEPDJ9qP4+IsjaHa0XT4tlyugVCoiBolSqRRjhhTjB/MnYkj/wt4unajbEvV+nUr9jT0t9TQ1NeHQCQv+stEqGlco5DDmZuFH5w/AEGN2gqojoniKx3t2KvWsrmBfSy+CIKDKYsX/vm4KO6ZUKjF/hBGD8jMSUBkRxUJX37O79VG60WiE0WgUjZ199tndeSoi6sSpsxsbmp3YuOMYtu2rREurBwA6nd2Yq83AmKElOHt0f4wfXgqVkms2EnUV+xvFgyAIaGpqQnVtfYTAse2DowevGsNZ6EQUFfYsSlaCIKCurg6v7g8PHLMz1Fg8pR9kUvY8or6A1+8QJZlGmxPHq+rwzdFKHDpmQaXFhiprx40GIs9ufOiO76G8JL83yyUiotMQBAGNjY1oamrCAx/UiI4plQooFAr84QcMHImIKD0IggCr1YqqBjv8Ha6pVKlU+OHEUgaORH0IQ0eiJFBtbcbnOw9j0/ZvcaK6Hj6fN+L9JBIpVP+/vXuPkqus84X/3XW/37rr2ulOQoAkoISQkAjyCpEcY1Au4nhZLzIROVF8ExTiQomjMHCcFVAXZuRlJs6ZEUYPvDAzHsJ40CgTuagkEQJRhCQSSOjQ1VXV97rf9n7eP5puqFRVdyeprl27+vtZq1dSz1OXX4VQv+xvPfvZZtPk6kavy4YrPvR+fPCCRQh28DQUIqJWIoTA4OAg3ugbxGMvV672MJlMMBqN+OZVS9DpNKtUIRERUeMIIRCPx5FMpfDigFIxZzab8VfLIrCZ6u9BT0Tth6EjUZMJIRAdGMMz+w6jfzCJF/98DKWyDFlWUCwWoChKzccZjeMrYiZWw6w4Zz6+8d/XQc+rvRERtRxFUfD8q734//a+jeGsXDFnNptgMBjxqVXzcEbAoVKFREREjSOEQCwWQyaTQSwrkC69u8zRYjbD57Ag5OKXbERzDUNHollULstIZQs4cPA4Dr7Zj/hQEn3xUYwks5P3EQIolYoolUo1n2NidaPRaESnx46Lzj8DV65ZBq+LGy8TEbUiIQTu3flH/Ol4smpuInAMuMxYd16oxqOJiIi0RVEUxGIxZLPjxzjHUpWBo95gwPol3AKKaC5i6EjUQGOpHP5r70GMjGXx+lsJvHl8AMoUF4ivt7rRZDTA57IiHPBiflcAixeG8MELFsFk5P+yREStTAiBlw69VSdwNMNkNOCTF87DR94fVKE6IiKixlIUBf39/cjlcgCATElgID9+/GOxWKDX63FWpw0eKy9uSTQXMcEgOgnlsoy+xBjS2TxyhRJGk1mMJLMYTWZx6Ggcx/oGZ/Q89VY32iwm/PXHl+O8xfMQCYdgsVhm420QEdEsyBXLeOy3h/GrP1f2AkkaDxyXzffhxssWwmnhgRcREWnfewPHsiLw52EFb6UrA0cAWDGPe88TzVWaCx0feOABfO9730MsFsOyZctw//33Y9WqVWqXRRohhECpLKNQLCNfKKFQKqNYLKNQLKNQKiOTK2I0mUWuUEJ8MImRZAbpbAGZbAHpXBHpbP09F2dqYnWjzWJEuMMDg16HdRefjXkBN9xOC7xeL7xeL3Q67tVIRKQFQgj850t9+N/7jqFYqty/cTxwtOBvrjkXZwa5fyMREbUHWZbR39+PfD4PAHhlWEFvWkCSJJjN5snAcYHPylWORHOYpkLHxx57DFu2bMGOHTuwevVqbN++HevWrcPhw4cRCATULo+aoFyWkc0XkckVMZLMIpsvolgqo1SS8ebxQRTLZRRLMlLpPEZT2clgsfBOsFgslVWpWwJw5vwAeoIudLqM6Aq4EfDZJy8KA4xfyTQQCHB1IxGRhrx0bAT/63dvITGagixXfiklSUDA68Q3rz4HARc/24mIqD3IsoxoNIpCoTA5VitwNOgkfKDHrVaZRNQCNBU63nfffdi4cSNuuOEGAMCOHTvw5JNP4sc//jFuv/32WX3tvX98E7n8u6fCivfs0ydQvWffxHTF/cSJ96k/997nbcxz1JgT0z8/AChCQFEUyIqAUN79vaIIKEKBLL/3VwFZVt55zPh9FUVArvNr5e/r3Xd8riwryBdqX2ylFX3gvIX4yCXnoifsg0EnMDI8hGKxWPO+Xq8XPp+vIoQkIqLW9uzBAfzkd8eQz+erVsFL0vipZXd84n3wOUwqVUhERNRYtQLHgdx44GixWCbP1rIZ9bhiaSdXORLNcZoJHYvFIvbv34+tW7dOjul0OqxduxZ79uyZ9df/6X/uRWywelN4mptsFhOsFiOsZhOCHS64nBb4vU6EOl04e0EQYf/4N3qKomBkZATxkZGaz2MymRAMBmE2m5tZPhERnabYaB4/+d1R5PPV2264rQZ8cGkYV6/shosHW0RE1CbK5TKi0WjFQopUUWBPQqkIHAHgk+cFYTfp1SiTiFqIZkLHwcFByLKMYLDyao/BYBCHDh2q+ZhCoVDxDUwyydCQqun1OpiNBphNBljNRnhcNtitZlgtRswLeeG0WWC3meGwmeGwmhHsdMFhmz4kzOfziMfjVReLmeDz+eD1erm6kYiohQkhcGwwi7eHs+gfzSOZK+GtwSyiI9l3VjhWniLw6Qs68LHVZ8Nk4upGIiJqH+VyGX19fRXHNvmywNP91YHjfK+FgSMRAdBQ6Hgqtm3bhrvuukvtMmiWmIwGuBwWmAx6mExGmIx6mIx6ZPMlrD5vIdwOC2xWM8wmA8xGAyxmA0xG4/jtd8ZMRj0MhsY2REVRMDw8jNHR0ZrzZrMZgUCAqxuJiFpYoSTjl3+KYdcfYyifECwKoSCXy1dsTwIAt3+kC0sX9TBwJCKitlIqlRCNRicDR1kIvDYicDQlqgJHr9WA/3Z2p1qlElGL0Uzo2NnZCb1ej3g8XjEej8cRCoVqPmbr1q3YsmXL5O1kMonu7u5Tev2esA8263hIVGtd2sRqtVqL1t67ku3EVW3vvSlhps8xxVyN6iamT/U5JGl8NaAkSdDrddBV/CpBJ+kmf9XpJOh1EnQ6HaT3/L7uY3QnPF4vnXDfyl8ddgvsVhPsVhNMRkPLrRLM5XJIJBI1VzdKkjR5ZepWq5uIiN51bCCD7//iMPIlpWpOURTk89WB4+dWBXDOmfNhNPJ0aiIiah+lUgl9fX0ol8cvyFlWBP6QUDBUQFXgCAAfPycAg47HOkQ0TjOho8lkwooVK7B7925cc801AMb/4b97925s3ry55mPMZnPDVpN9479/tCHPQ+2JqxuJiLRJCIGD0RSODWQwnCniYDSJ+Fih5n1rBY4LO8z4+Pt9WHXuGTAYNPPPKiIiomkVi0VEo9HJwBEADo+J8cDRaq1aSLF+SSdPqyaiCpr61/GWLVuwYcMGrFy5EqtWrcL27duRyWQmr2ZNpIbpVjf6fD54PB6ubiQiahGjmSL2HxvBULqIX78Sn/4BGA8cI3YBf9AGl0WPTocBC3xmuO0WdHV1Qa/nQRYREbWPYrGIvr4+yLIMAEjkBI6nFURzUlXgaDPq8eEzfZjnsahVLhG1KE2Fjp/5zGcwMDCAO+64A7FYDOeffz527dpVdXEZomZQFAVDQ0MYGxurOW82mxEMBrm3FxFRi0jlS9j9agK/fiWOYrn61Ol6/q+zvFgRVGAxVH55ZDabEYlEGDgSEVFbKRQKiEajk4HjK8MK3kwq0Ol0sFgsFYHjog4r1p7VwQUWRFSTpkJHANi8eXPd06mJmiWbzSKRSFScajCBqxuJiFrH28NZ/PntJOJjeex5fajqojDT+dKl3fDp0hCi8vPcYrEgEolU7WVFRESkZfl8HtFoFIoy/uVcf7Z+4AgA7w85ecxDRHVpLnQkUtN0qxstFgsCgQBXNxIRqUxWBB7d24unXxuY8WNsZj0uPycAn8MEv9OMeS4d4vF41UVjrFYrwuEwA0ciImorJwaORVngpYH6gWOX24yAk8c9RFQfQ0eiGZpudWNHRwfcbje/6SMiUlkqX8L/fPooXutLTnm/xWEnejps8NiMWNrlQk+HbXIunU7XDBxtNhtCoRADRyIiaiu5XA7RaHSy7wkh8HRUhtDpYTGbK45xPnJ2BxxmA/x2I499iGhKDB2JpqEoCgYHB5FM1j545epGIqLW0DuUxc9fiuLVvuSUezaeO8+FT6/qRpfPWnM+lUohHq++wIzD4UAwGOQBFhERtZVsNov+/v7JwLEgC+yNKyhBD/N7AkebUY/rV4TZB4loxhg6Ek2BqxuJiLThSDyN7//iMMpy7T0bF4edOHeeC4tDTiwKOuo+TzKZRCKRqBp3Op0IBAL8vCcioraSyWQQi8UghIAQAkMF4A8JGYpUGTgCwOVn+dgHieik8NwgohpkWUYikUA0Gq0ZOFqtVvT09PBiMURU13PPPYcrr7wSkUgEkiRh586dFfNCCNxxxx0Ih8OwWq1Yu3YtXn/9dXWK1bhkroQf7PpLzcDRZTXgm1ctwW0fW4wrloWnDBxHR0drBo4ul4uBIxERtZ2JwFFRFLyVUvCL4zJ+HxsPHE88pXp1jxtdbouK1RKRFjF0JDpBJpPB8ePHa55OLUkS/H4/IpEIjEajCtURkVZkMhksW7YMDzzwQM357373u/jhD3+IHTt2YN++fbDb7Vi3bh3y+XyTK9W2fFHG/9j5Ggql6tOpP3CmD9+6+hycEagfNE4YGRnB4OBg1bjH44Hf72fgSEREbSWdTqO/vx/5soLfRBUcGFJQVgCDwQCL2Qy80/dMegkfX+rH8i6XyhUTkRbx9Gqid8iyjMHBQaRSqZrzVqsVgUCAYSMRzcj69euxfv36mnNCCGzfvh3f+ta3cPXVVwMAfvKTnyAYDGLnzp347Gc/28xSNeulYyP4h/96o2rcYzPim1cthc8x/V67QgiMjIxgeHi4as7r9cLn46lkRETUXib2LhZC4HcxBenS+JkCBoMBZpNpMnC0GnW4+twAPFYe/xDRqWHoSITxFUmJRAKyLFfNSZKEzs5OuFwuHngSUUMcPXoUsVgMa9eunRxzu91YvXo19uzZUzN0LBQKKBQKk7frXdyq3QkhcDCawv5jI3j24EDVvFEv4VtXL4XHPrPAcWhoCKOjo1VzPp8PPp+vESUTERG1jLGxMbz+dgJ5WSCRE3UDx4U+K1Z1uxk4EtFpYehIcxpXNxKRGmKxGAAgGAxWjAeDwcm5E23btg133XXXrNfWyoplBd978jCODmRqzut1Ev6ftWfOOHAcHBzE2NhY1VxnZyc8Hs/plktERNQyUoUyfvd6HK/Fqo97jAYDTO8Ejov9dqzuccNm0qtQJRG1G4aONGel02kMDAzUXN2o0+nQ2dkJp9PJ1Y1E1BK2bt2KLVu2TN5OJpPo7u5WsaLmOfDWKJ45mMCbiQyyxerPbAAw6CR87YqzcVbIOe3zCSEwMDBQc7Wo3++H2+0+7ZqJiIjUVJIVZIoyirJA31gee48OIZsvVN3PaDTCZDQCkgSP1YA1Z3KVPxE1DkNHmnNkWcbAwADS6XTNeZvNhkAgAIOB/3sQ0ewIhUIAgHg8jnA4PDkej8dx/vnn13yM2WyG2WxuRnktoVhW8PKxEfzsxT4Mp4tT3rfLa8XWK5fAMoNVGUIIxOPxmj0gGAzC6Zw+tCQiImpVJVnBM28M442h3LtjpRKKxepe+t7AEQAumu9pVplENEcwVaE5hasbiagVLFy4EKFQCLt3754MGZPJJPbt24cvf/nL6hanIiEEnn99CM+/PoTD/bW3vTjRjZcuxIqFXpgMuhk9fywWQyZTfXp2KBSCwzH9Va6JiIhaTa4kI5osIF9S8NujI+9OCIFiqYRSqVT1GKPRCIfVgm6PBV6bAYt8Nnht3FKKiBqLoSPNCVzdSETNlk6nceTIkcnbR48exYEDB+Dz+dDT04NbbrkF3/nOd3DWWWdh4cKF+Pa3v41IJIJrrrlGvaJVlCmU8dBzx/DyW6PT3vecLhc+vjyMs2dwKvUERVEQi8WQzWYrxiVJQigUgt1uP9mSiYiIVDecLWHnn+MoyqJyok7g2GWX8L4uL5bO80Ov40ILIppdTFiorQkhJlc3KopSNa/T6eD3++FwOLi6kYga6sUXX8SaNWsmb0/sx7hhwwY89NBD+PrXv45MJoMvfvGLGB0dxSWXXIJdu3bBYrGoVbJqxrIl3PPzQxhIVe819V4fPieAdecF0eE4udPMFUVBf38/crlcxbgkSQiHw7DZbCddMxERkdpGcyU88Wpi2sDRrAcCVgkLHDqcPc/Pi6URUdMwdKS2VS6XMTAwUPM0OgCw2+3w+/1c3UhEs+Kyyy6DEKLuvCRJuPvuu3H33Xc3sarW9Oje3ikDx/Pne3DFshDOCJz86c+yLKO/vx/5fL5iXKfTIRwOw2q1nvRzEhERqSmWKuDlviTeGslXTwqBYrGIUrmMoFXC6oBucnEFL5ZGRM3GtIXaDlc3EhFpx6FoEi+8OVIxZjPrsWZpAGf47TgjaIfTcmp7TMmyjGg0ikKhMtDU6XSIRCJzclUpERFpU6pQxttjebw+kEU0WeeLOiFQKBYRscjwmnXotkuTxzuBQAAul6uJFRMRAdPvuk6kIeVyGbFYDPF4vGbgaLfb0dPTw4vFEBGpKFso4/d/GcT2XX/B93/xl4o5q0mPv/3EufjEyi4sm+855cCxXC6jr6+vKnDU6/Xo6upi4EhE9I7nnnsOV155JSKRCCRJws6dO6vuc/DgQVx11VVwu92w2+248MIL0dvbOzmfz+exadMmdHR0wOFw4JOf/CTi8XgT30V7khWBP/SO4ZGX+/HwS/149o2RKQPHcqmINSGB5Z16LHDqJvdsDAaDDByJSBVc6UhtQQiBVCqFwcHBmmGjXq+H3++H3W5n2EhE1CTRkRx2/SmGwdT4FTXzJRn5koxMQYas1D71/CPvD8LnMJ3W604Ejidunj8ROJpMp/f8RETtJJPJYNmyZfjCF76Aa6+9tmr+jTfewCWXXIIbb7wRd911F1wuF1599dWKL29uvfVWPPnkk/j3f/93uN1ubN68Gddeey1+//vfN/OttJ3n3xrFq7HaF8KcYNRLCDpMkIo5BI0CNkPlsU4oFILDcfLbkxARNQJDR9K8crmMRCJRdUXSCQ6HA36/H3q9vsmVERHNXWVZwX2//AtGs6Xp7/wOp8WA/3Zu8LRet1Qqoa+vD+VyuWLcYDCgq6sLRuOprZwkImpX69evx/r16+vO/83f/A2uuOIKfPe7350cW7Ro0eTvx8bG8C//8i945JFH8OEPfxgA8OCDD2Lp0qXYu3cvPvCBD8xe8W2qrAi8cHxsysDRZtRjWcSJpQEbhgYSyGRKAN4NHCVJQigUgt1ub0LFRES18fRq0iwhBJLJJHp7e2sGjnq9HqFQCKFQiIEjEVGTvT2cm3HgaNBLODPowM0fORMW06l/XheLxZqBo9FoZOBIRHQKFEXBk08+ibPPPhvr1q1DIBDA6tWrK07B3r9/P0qlEtauXTs5tmTJEvT09GDPnj11n7tQKCCZTFb8EBBN5vHvf4zhj9FU1ZzZoMOiDivWLPLh/74gjPeH7BhMxKsunMnAkYhaBVc6kiaVSiUMDAxwdSMRUYuaLnA06CS8r9uNVWf4sKzHDbPx9D6vC4UCotEoZFmuGDeZTIhEIjAY+E8eIqKTlUgkkE6ncc899+A73/kO7r33XuzatQvXXnstnn76aVx66aWIxWIwmUzweDwVjw0Gg4jFYnWfe9u2bbjrrrtm+R1oR0lW8PyxURxMZGrOLw3a8aGF3smtohRFQX9/P3K5XMX9JElCOByGzWab9ZqJiKbDf4GTpkysbhwaGqq7d2MgEOC3ekREKhvJFCtuB91mXLtyHixGHawmPUJuC2zmxvwzJJ/PIxqNVvUFs9mMSCTCL6CIiE7RxOfq1VdfjVtvvRUAcP755+P555/Hjh07cOmll57yc2/duhVbtmyZvJ1MJtHd3X16BWuUEAL/9foQ3hrJV83pJOCCeS6s6HJVBI7RaBT5fOX9dTodwuEwrFZrU+omIpoOQ0fSjFKphEQiUfVt3gSn04nOzk4eXBIRtYATVzp2ea1YsdDb8NfJ5XLo7++vChwtFgvC4TB7AhHRaejs7ITBYMA555xTMb506VL87ne/AzB+oZJisYjR0dGK1Y7xeByhUKjuc5vNZpjN5lmpW2uOj+ZrBo4BhwmXnuFFh/3dC6DJsoz+/v6agWMkEqm4wA8Rkdq4pyO1PCEExsbG0NvbWzNw1Ov1CIfDCAaDPLgkImoBh6JJ/Oa1RMWYx9b4K0Zns9maKxytVitXOBIRNYDJZMKFF16Iw4cPV4z/5S9/wfz58wEAK1asgNFoxO7duyfnDx8+jN7eXlx00UVNrVerekerA8cPLvDgmvcFqgLHeiscu7q6GDgSUcvhSkdqaVzdSESkLfuPjuB/Pv0myoqoGO/yNvZUr0wmg1gsBiEqX8dqtSIcDkOn4/eqREQzkU6nceTIkcnbR48exYEDB+Dz+dDT04PbbrsNn/nMZ/ChD30Ia9aswa5du/Dzn/8czzzzDADA7XbjxhtvxJYtW+Dz+eByuXDzzTfjoosu4pWrZ6goV355tthvx/vDzooxWZbR19eHYrFy+xK9Xo9IJMJVo0TUkhg6UkuaWN04NDRUdUAJAAaDAX6/n3s3EhG1kGcOJvDw87048WP77JADF5/d0bDXSafTiMfjVf3BbrcjGAwycCQiOgkvvvgi1qxZM3l7Yp/FDRs24KGHHsInPvEJ7NixA9u2bcNXvvIVLF68GD/72c9wySWXTD7mBz/4AXQ6HT75yU+iUChg3bp1+Id/+Iemv5dWN5wt4Y2hLPJlBbIiUFYEZEUgnqoMEu2mygUV5XIZ0Wi0ZuDY1dUFk6nxZxMQETWCJGolOm0qmUzC7XZjbGwMLpdL7XKojlKphHg8XnXawASXy4WOjg6ubiRqY/y8nl4r/RkJIfCfL0Xx85f7q+aWL/Bg42VnwGRoTBCYSqUQj8erxh0OB4LB4OQm+0REraSVPrNbVbv/Gb0WT+O5N0dmdN+V3S6snOcGMB449vX1oVSq3CvZYDAgEokwcCQiVcz0M5srHallzGR1YyAQgM1mU6E6IiKqRVEE/tfzb+G5Q4NVcx9a0onPXTwfOl1jgsBkMolEIlE17nQ6EQgEGDgSEVFLyhZl/P7Y6Izvb3nni7pSqYS+vj6Uy+WKeYPBgK6uLhiNxkaWSUTUcAwdqSUUi0UkEokpVzd2dnbylDkiohZSLCv452fexEs1DqSuXB7GVRdEGhYEjo6OYnCwOth0u93o7Oxk4EhERC3r2EgOsjKzEwxtRj0WeK11A0ej0Yiuri4YDDyUJ6LWx08qUpUQAqOjoxgeHubqRiIiDckWyvh/nzqCv8TSFeOSBFx3cQ8uWxpo2GuNjIxgaGioatzj8aCjo4OBIxERtbREulg1dl7YAZ0kwaCXoJckGHQSzAYduj0W6IWMt9/ugyzLFY8xmUyIRCIMHIlIM/hpRaqZbnWj2+1GR0cHVzcSETVJoSwjk5dRkhWUZAXFsoKSLMZvv/P74ju/f/bQAN4ezlU83qCTsHHNGVix0NuQeoQQGB4exshI9R5YXq8XPp+PgSMREbW8dKEyPFzd48byrtp7oBUKBfRFozUDx66uLu5rT0SawtCRmm661Y1GoxGBQABWq1WF6oiI5q69rw/jp79/65QeazXpsWntIiyJNGbzfyEEhoaGMDo6WjXX0dEBr7cxwSYREdFsemskh/5UoWLsxKtTTygUCujr64OiKBXjZrMZkUiEgSMRaQ5DR2qqQqGARCKBQqFQc56rG4mI1HOqV5h224y4Zd1Z6O5ozFYYQggMDg5ibGysaq6zsxMej6chr0NERDSbjgxm8ZsjQzhxO0evtfoCMPl8HtFotCpwtFgsCIfDDByJSJMYOlJTCCEwMjKCkZERrm4kImpRBv3Jn6occJlx6/qz4XeaG1KDEAKJRAKpVKpqzu/3w+12N+R1iIiIZtOrsTR+e7R6e5BFHVZ02itDx1wuh/7+/pqBYyQS4YIMItIsho4066Zb3ejxeODz+dhMiYhUZtK/+zksSeN7NJoMOhj1OpgMOhj047cNuvHbEY8FH1sehtNSvWLjVAghEI/HkU6nq+aCwSCcTmdDXoeIiGg2vdyXxL7e6tX6Z/ttuGxR5X7EuVwO0Wi0amGG1WpFOBzmMRIRaRpDR5o1E6sbh4eHa84bjUYEg0FYLJYmV0ZERLWcO8+FH15/PowGHQw6qakXaRFCIBaLIZPJVIxLkoRgMAiHw9G0WoiIiGZCVgTG8mWMZEsYyZcwmi1jOFfCcLZUdd/3hRz44AJPRW/NZrPo7++vChxtNhtCoRADRyLSPIaONCsKhQLi8TiKxWLNea5uJCJqPQa9DgZ98z+XFUVBLBZDNputGJckCaFQCHa7vek1ERER1SKEwBtDOfwxmsJApvaxzolWznNhxTxXReCYyWQQi8WqAke73Y5QKNTUL/6IiGYLQ0dqKCEEhoeHMTJSvX8JAJhMJgQCAa5uJCIiAOOBY39/P3K5XMW4JEkIh8Ow2RpzcRoiIqLTIYRA72geLxwfw2CmeiVjPRcv8OC8cOX2IOl0GvF4nIEjEbU9ho7UMPl8HolEou7qRq/XC5/PxyZKREQAAFmW0d/fj3w+XzGu0+kQDod5cTEiImoqIQTKikChrKAoCxTLCgqygnxZwcF4BrFU7T3qazEbdPjgAg/O9leu1k+lUojH41X3dzgcCAaDPFYiorbC0JFOG1c3EhHRyZJlGdFotOoiYzqdDpFIhD2DiIhOy2iuhGxJRrEsUJCVyQCxWBYoyso7waIyOV8oKyjJChQx/XOfyG7Sw2s1wGM1wms1wmM1IOAwwXjCliXJZBKJRKLq8U6nE4FAgIEjEbUdho50Wri6kYiITla5XEY0Gq3qHXq9HpFIBGazWaXKiIhI62RF4P8cHEB/cuarEk+F12rAhd1uzPNYYJrBfshjY2MYGBioGne5XPD7/TxeIqK2xNCRTomiKBgeHsbo6GjNeZPJhGAwyANHIiKqUCqVEI1GUSpV7oel1+vR1dUFk8mkUmVERNQODiUysxo4Os16rOx246xOG3QzDApHR0cxODhYNe52u9HZ2cnAkYjaFkNHOmn5fB7xeLzqgHGCz+eD1+tl8yQiogqlUgl9fX0ol8sV4waDAV1dXTAajSpVRkRE7eL4aH76O82QUSfBZNDBpNfBZtLhDJ8NSwJ26HUzP84ZGRnB0NBQ1bjH40FHRwePmYiorTF0pBmbbnWj2WxGIBDg6kYiIqpSLBbR19cHWZYrxo1GI7q6umAw8J8kRER0eoQQ6D/hYi82ox4203hwaDLoYNbrYNJL7/7eMH7b/E64aDa8Oz/TlYz1DA8PY3h4uGqcW1AR0VzBf+HTjORyOSQSiZqrGyVJgtfr5epGIiKqqVAoIBqNVgWOJpMJkUiEgSMRETXEcLaEQlmpGLv2/QE4zM3tM1NdaNPn88Hn8zW1HiIitfBf+TQlRVEwNDSEsbGxmvNc3UhERFPJ5/OIRqNQlMqDQLPZjEgkAr1er1JlRETUbqIn7OXoNOtVCRyHhoZqnh3W0dEBr9fb1HqIiNTE0JHqmm51o8/ng8fj4epGIiKqKZfLob+/vypwtFgsCIfDDByJiKihTryATMRlaerrCyEwODhYc8GG3++H2+1uaj1ERGpj6EhVplvdaLFYEAgEeIVRIiKqK5vNor+/H0KIinGr1YpwOAydTqdSZURE1I5q7ecYdjXvbCwhBAYGBpBMJqvmGDgS0VzF0JEqZLNZJBKJqiuLAlzdSEREM5PJZBCLxaoCR5vNhlAoxMCRiIgabjRfRq5UubI+0qTQUQiBRCKBVCpVNRcIBOByuZpSBxFRq2HoSADGVzcODg7W/GYO4OpGIiKamXQ6jVgsVjVut9sRCoX4pRUREc2KE0+ttpv0cJpnfxsPIQTi8TjS6XTVXDAYhNPpnPUaiIhaFUNHmnZ1Y0dHB9xuNw8UiYhoSqlUCvF4vGrc4XAgGAyyjxAR0aw58SIyYZd51vuOEAKxWAyZTKZiXJIkBINBOByOWX19IqJWx9BxDpNlGUNDQ1OubgwGgzAajU2ujIiItGZsbAwDAwNV406nE4FAgIEjERHNGiFEjYvIzO6p1VMFjqFQCHa7fVZfn4hICxg6zlGZTAYDAwNc3UhERKdtdHQUg4ODVeNutxudnZ3sJURENKuShTIyRblibDYvIqMoCmKxGLLZbMW4JEkIh8Ow2Wyz9tpERFrC0HGOkWUZg4ODNTc5BsavKhoIBLi6kYiIZmR4eBjDw8NV4x6PBx0dHQwciYho1sVTxYrbVqMOHsvsHOoqioL+/n7kcrmKcUmSEIlEYLVaZ+V1iYi0iKHjHJLJZJBIJCDLctWcJEno7OyEy+XiASIREU1LCIHh4WGMjIxUzfl8Pni9XvYTIiJqilyp8vimw2aclR6kKAqi0Sjy+XzFuE6nQzgcZuBIRHQCho5zAFc3EhFRIwkhMDQ0hNHR0aq5jo4OeL3e5hdFRERzVq6kVNy2GBp/1WpZlhGNRlEoVO4dqdPpEIlEYLFYGv6aRERax9CxzU21ulGn06Gjo4OrG4mIaMaEEBgYGKh5EbLOzk54PJ7mF0VERHNavnxC6GjUNfT5pwocu7q6YDbP7kVriIi0iqFjm5JlGQMDA0in0zXnbTYb/H4/VzcSEdGMCSGQSCRqrpwPBAJwuVwqVEVERHOdrIiK2xZD40JHWZbR19eHYrFy30i9Xo9IJMLAkYhoCgwd21A6ncbAwEDd1Y2dnZ1wOp1c3UhERDMmhEA8Hq/5ZVYwGITT6VShKiIiIuDyszqw5kwfimUF+bICo74xoWO5XEZfXx9KpVLFuF6vR1dXF0wmU0Neh4ioXTF0bCMzWd0YCARgMPA/OxERzZyiKIjH48hkMhXjkiQhGAzC4XCoVBkREdE4nSTBYtTDYmzMfo71AkeDwYCuri6eMUZENANMn9qAEAKZTIarG4mIqOEURUF/fz9yuVzFuCRJCIVCsNvtKlVGREQ0O0qlEvr6+lAulyvGGTgSEZ2cxu6wO4sWLFgASZIqfu655x61y1JduVxGLBZDLBarGTja7Xb09PTwYjFERHTSFEVBNBqtGTiGw2EGjkRE1HaKxWLNwNFoNGLevHkMHImIToKmVjrefffd2Lhx4+Ttubx/lBBicu9GRVGq5nU6Hfx+PxwOB8NGIiI6aVNdqTMcDsNqtapUGRER0eyYCBxPXMxhMpkQiUS4TRUR0UnS1Kem0+lEKBRSuwzVlctlDAwMVO2tNcFut8Pv97MpEhHRKZkqcIxEIrBYLCpVRkRENDsKhQKi0WjNwLGrqwt6fWP2iiQimks0c3o1ANxzzz3o6OjA8uXL8b3vfa9qyfuJCoUCkslkxY+WCSGQSqXQ29tbM3DU6XQIBoMIhUIMHImI6JRMbJx/YuA4caVOBo5ERNRuCoVCzRWOZrOZgSMR0WnQTDL1la98BRdccAF8Ph+ef/55bN26Ff39/bjvvvvqPmbbtm246667mljl7CmXy0gkEshmszXnHQ4H/H4/GyIREZ2yUqmEaDRa80qdkUgEJpNJpcqIiIhmRz6fRzQardqyymKxIBwO8/iKiOg0SEIIodaL33777bj33nunvM/BgwexZMmSqvEf//jH+NKXvoR0Og2z2VzzsYVCoWKlRjKZRHd3N8bGxuByuU6v+CaZWN04ODhYc+9GvV4/uXcjEVG7SCaTcLvdmvq8brZG/xnxSp1ERLOHfW16avwZ5XI5RKNRnHhIbLVaEQ6HodNp6sRAIqKmmelntqorHb/2ta/h85///JT3OeOMM2qOr169GuVyGceOHcPixYtr3sdsNtcNJLWAqxuJiKgZ6m2cbzQa0dXVxS07iIio7WSzWfT39zNwJCKaRap+kvr9fixZsmTKn3qnch04cAA6nQ6BQKDJVc8+IQSSySR6e3trBo56vR6hUAihUIiBIxERnZZ6+1hNbJzPwJGIqL0999xzuPLKKxGJRCBJEnbu3Fn3vjfddBMkScL27dsrxoeHh3HdddfB5XLB4/HgxhtvRDqdnt3CT0O9wNFmszFwJCJqIE0cSezZswf79u3DmjVr4HQ6sWfPHtx666343Oc+B6/Xq3Z5DVUqlZBIJJDL5WrOO51OdHZ2MmwkIqLTVm8fK7PZjEgkwl5DRDQHZDIZLFu2DF/4whdw7bXX1r3f448/jr179yISiVTNXXfddejv78dTTz2FUqmEG264AV/84hfxyCOPzGbppySTySAWi1UFjna7HaFQCJIkqVQZEVH70UToaDab8eijj+Jv//ZvUSgUsHDhQtx6663YsmWL2qU1zMTqxsHBwaoGCIyvbgwEArDb7SpUR0RE7abePlbcOJ+IaG5Zv3491q9fP+V9+vr6cPPNN+NXv/oVPvaxj1XMHTx4ELt27cILL7yAlStXAgDuv/9+XHHFFfj+979fM6RUSzqdRiwWqxp3OBwIBoMMHImIGkwT68YvuOAC7N27F6Ojo8jlcnjttdewdetWTe/X+F6yLCMajWJgYKBm4Oh0OtHT08PAkYioDT3wwANYsGABLBYLVq9ejT/84Q+z/prZbLbuxvlc4UhERO+lKAquv/563HbbbTj33HOr5vfs2QOPxzMZOALA2rVrodPpsG/fvrrPWygUkEwmK35mUyqVqhk4Op1OBo5ERLNEE6Fju9PpdDWvTG0wGBAOhxEMBnkASETUhh577DFs2bIFd955J1566SUsW7YM69atQyKRmLXXFEJgaGiI+1gREdGM3HvvvTAYDPjKV75Scz4Wi1Xts28wGODz+WqGfBO2bdsGt9s9+dPd3d3Qut9LURQMDQ1VjbtcLgQCAQaORESzhEcWLUCSpKpm53K50N3dzdWNRERt7L777sPGjRtxww034JxzzsGOHTtgs9nw4x//eNZeU5IkRCIRGI3GyTG73c7AkYiIquzfvx9///d/j4ceeqjhwdzWrVsxNjY2+XP8+PGGPv976XS6qpX8brcbfr+fgSMR0Szi0UWLMJvN8Hq9MBgMiEQiCAQCXN1IRNTGisUi9u/fj7Vr106O6XQ6rF27Fnv27JnV19br9ejq6oLRaITD4eDG+UREVNNvf/tbJBIJ9PT0wGAwwGAw4K233sLXvvY1LFiwAAAQCoWqVuiXy2UMDw8jFArVfW6z2QyXy1XxM5tMJhO6urqg1+vh8XjQ2dnJ3kdENMs0cSGZucLr9cLj8XClCRHRHDA4OAhZlhEMBivGg8EgDh06VHX/QqGAQqEweft0974yGAyTB1886CIiolquv/76ii/HAGDdunW4/vrrccMNNwAALrroIoyOjmL//v1YsWIFAOA3v/kNFEXB6tWrm17zVEwmE7q7u9n7iIiahKFjC5Ekic2PiIhq2rZtG+66666GPqfBwH8GEBHNdel0GkeOHJm8ffToURw4cAA+nw89PT3o6OiouL/RaEQoFMLixYsBAEuXLsVHP/pRbNy4ETt27ECpVMLmzZvx2c9+tqWuXD2BvY+IqHm4pI6IiEgFnZ2d0Ov1iMfjFePxeLzm6WjN3PuKiIjmjhdffBHLly/H8uXLAQBbtmzB8uXLcccdd8z4OR5++GEsWbIEl19+Oa644gpccskl+Kd/+qfZKpmIiDSCX/MQERGpwGQyYcWKFdi9ezeuueYaAONX19y9ezc2b95cdX+z2Qyz2dzkKomIqN1ddtllEELM+P7Hjh2rGvP5fHjkkUcaWBUREbUDho5EREQq2bJlCzZs2ICVK1di1apV2L59OzKZzOQ+WURERERERFrF0JGIiEgln/nMZzAwMIA77rgDsVgM559/Pnbt2lV1cRkiIiIiIiKtYehIRESkos2bN9c8nZqIiIiIiEjLeCEZIiIiIiIiIiIiaiiGjkRERERERERERNRQDB2JiIiIiIiIiIiooRg6EhERERERERERUUMxdCQiIiIiIiIiIqKGmlNXrxZCAACSyaTKlRAR0VQmPqcnPrepGnsaEZF2sK9Nj32NiEg7ZtrX5lTomEqlAADd3d0qV0JERDORSqXgdrvVLqMlsacREWkP+1p97GtERNozXV+TxBz6uk1RFESjUTidTkiSdMrPk0wm0d3djePHj8PlcjWwwtnH2tXB2tWh5doBbdd/urULIZBKpRCJRKDTcSeQWhrV0wDt/l1j3c3FupuLdTdPM2pmX5teI/vaTGnx7+tU2u39AO33nvh+Wlu7vR9g9t7TTPvanFrpqNPpMG/evIY9n8vl0uxfRNauDtauDi3XDmi7/tOpnStBptbongZo9+8a624u1t1crLt5Zrtm9rWpzUZfmykt/n2dSru9H6D93hPfT2trt/cDzM57mklf49dsRERERERERERE1FAMHYmIiIiIiIiIiKihGDqeArPZjDvvvBNms1ntUk4aa1cHa1eHlmsHtF2/lmufi7T634t1Nxfrbi7W3TxarJkao93+27fb+wHa7z3x/bS2dns/gPrvaU5dSIaIiIiIiIiIiIhmH1c6EhERERERERERUUMxdCQiIiIiIiIiIqKGYuhIREREREREREREDcXQkYiIiIiIiIiIiBqKoWODFAoFnH/++ZAkCQcOHFC7nBm56qqr0NPTA4vFgnA4jOuvvx7RaFTtsqZ17Ngx3HjjjVi4cCGsVisWLVqEO++8E8ViUe3SZuTv/u7vcPHFF8Nms8Hj8ahdzrQeeOABLFiwABaLBatXr8Yf/vAHtUua1nPPPYcrr7wSkUgEkiRh586dapc0Y9u2bcOFF14Ip9OJQCCAa665BocPH1a7rBn5x3/8R5x33nlwuVxwuVy46KKL8Mtf/lLtsugUaK0/aLkvaKUnsBc0h1Z7QLt8/t9zzz2QJAm33HKL2qWQSrTW/6ai5d5Yj1Z6Zj1a7KX1aLHHTkWr/beeVurLDB0b5Otf/zoikYjaZZyUNWvW4N/+7d9w+PBh/OxnP8Mbb7yBv/qrv1K7rGkdOnQIiqLgRz/6EV599VX84Ac/wI4dO/DNb35T7dJmpFgs4lOf+hS+/OUvq13KtB577DFs2bIFd955J1566SUsW7YM69atQyKRULu0KWUyGSxbtgwPPPCA2qWctGeffRabNm3C3r178dRTT6FUKuEjH/kIMpmM2qVNa968ebjnnnuwf/9+vPjii/jwhz+Mq6++Gq+++qrapdFJ0lp/0HJf0EJPYC9oHq32gHb4/H/hhRfwox/9COedd57apZCKtNb/pqLl3liPFnpmPVrtpfVoscdORav9t56W6suCTtsvfvELsWTJEvHqq68KAOLll19Wu6RT8sQTTwhJkkSxWFS7lJP23e9+VyxcuFDtMk7Kgw8+KNxut9plTGnVqlVi06ZNk7dlWRaRSERs27ZNxapODgDx+OOPq13GKUskEgKAePbZZ9Uu5ZR4vV7xz//8z2qXQadJi/1Ba32hlXsCe4F6tNwDtPT5n0qlxFlnnSWeeuopcemll4qvfvWrapdELUKL/W8qWuuN9bRyz6ynHXppPVrtsVPRcv+tR62+zJWOpykej2Pjxo346U9/CpvNpnY5p2x4eBgPP/wwLr74YhiNRrXLOWljY2Pw+Xxql9FWisUi9u/fj7Vr106O6XQ6rF27Fnv27FGxsrllbGwMADT391uWZTz66KPIZDK46KKL1C6HToNW+wP7QmOwF6hLiz1Ai5//mzZtwsc+9rGKv+dEWu1/U2FvVAd7qfZosf/Wo3ZfZuh4GoQQ+PznP4+bbroJK1euVLucU/KNb3wDdrsdHR0d6O3txRNPPKF2SSftyJEjuP/++/GlL31J7VLayuDgIGRZRjAYrBgPBoOIxWIqVTW3KIqCW265BR/84Afxvve9T+1yZuSVV16Bw+GA2WzGTTfdhMcffxznnHOO2mXRKdByf2BfaBz2AvVorQdo9fP/0UcfxUsvvYRt27apXQq1CC33v6mwN6qHvVRbtNZ/62mVvszQsYbbb78dkiRN+XPo0CHcf//9SKVS2Lp1q9olT5pp7RNuu+02vPzyy/j1r38NvV6Pv/7rv4YQQhO1A0BfXx8++tGP4lOf+hQ2btyoSt3AqdVONJ1Nmzbhz3/+Mx599FG1S5mxxYsX48CBA9i3bx++/OUvY8OGDXjttdfULougzf6g1b7AnkCNoLUeoMXP/+PHj+OrX/0qHn74YVgsFrXLoVmixf43Fa32xnrYM6nVaK3/1tMqfVkSrfQJ2iIGBgYwNDQ05X3OOOMMfPrTn8bPf/5zSJI0OS7LMvR6Pa677jr867/+62yXWmWmtZtMpqrxt99+G93d3Xj++edVWXZ7srVHo1Fcdtll+MAHPoCHHnoIOp16Gfqp/Lk/9NBDuOWWWzA6OjrL1Z2aYrEIm82G//iP/8A111wzOb5hwwaMjo5q5ltfSZLw+OOPV7wHLdi8eTOeeOIJPPfcc1i4cKHa5ZyytWvXYtGiRfjRj36kdilznhb7g1b7Qjv1BPYCdbRDD9DC5//OnTvxiU98Anq9fnJMlmVIkgSdTodCoVAxR9qkxf43Fa32xnraqWfW0y69tB6t9diptEP/rUetvmxo6qtphN/vh9/vn/Z+P/zhD/Gd73xn8nY0GsW6devw2GOPYfXq1bNZYl0zrb0WRVEAAIVCoZElzdjJ1N7X14c1a9ZgxYoVePDBB1Vvnqfz596qTCYTVqxYgd27d082EEVRsHv3bmzevFnd4tqYEAI333wzHn/8cTzzzDOab3aKoqj2mUKVtNgftNoX2qknsBc0Vzv1AC18/l9++eV45ZVXKsZuuOEGLFmyBN/4xjcYOLYJLfa/qWi1N9bTTj2zHvbS1tdO/bcetfoyQ8fT0NPTU3Hb4XAAABYtWoR58+apUdKM7du3Dy+88AIuueQSeL1evPHGG/j2t7+NRYsWtcy3ePX09fXhsssuw/z58/H9738fAwMDk3OhUEjFymamt7cXw8PD6O3thSzLOHDgAADgzDPPnPw71Cq2bNmCDRs2YOXKlVi1ahW2b9+OTCaDG264Qe3SppROp3HkyJHJ20ePHsWBAwfg8/mq/r9tNZs2bcIjjzyCJ554Ak6nc3KfF7fbDavVqnJ1U9u6dSvWr1+Pnp4epFIpPPLII3jmmWfwq1/9Su3S6CRosT9ouS9ooSewFzSPVnuAVj//nU5n1X5dE3v5aXkfLzo1Wux/U9Fyb6xHCz2zHq320nq02GOnotX+W09L9eWmXy+7jR09elQAEC+//LLapUzrT3/6k1izZo3w+XzCbDaLBQsWiJtuukm8/fbbapc2rQcffFAAqPmjBRs2bKhZ+9NPP612aTXdf//9oqenR5hMJrFq1Sqxd+9etUua1tNPP13zz3jDhg1qlzaten+3H3zwQbVLm9YXvvAFMX/+fGEymYTf7xeXX365+PWvf612WXSStNgftNwXtNIT2AuaQ6s9oJ0+/y+99FLx1a9+Ve0ySAVa7H9T0XJvrEcrPbMeLfbSerTYY6ei1f5bTyv1Ze7pSERERERERERERA3Veps6EBERERERERERkaYxdCQiIiIiIiIiIqKGYuhIREREREREREREDcXQkYiIiIiIiIiIiBqKoSMRERERERERERE1FENHIiIiIiIiIiIiaiiGjkRERERERERERNRQDB2JiIiIiIiIiIiooRg6EhERERERERERUUMxdCQiIiIiIiIiIqKGYuhIREREREREREREDcXQkYiIiIiIiIiIiBrq/wdXna7pyZ7c5AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1600x1000 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeExpoSamples()\n",
    "NormalPlotSamples(samples, plot=1, ylabel=\"sum of expo values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a347e4e",
   "metadata": {},
   "source": [
    "Figure [\\[normal1\\]](#normal1){reference-type=\"ref\" reference=\"normal1\"}\n",
    "(top row) shows the results. With `n=1`, the distribution of the sum is\n",
    "still exponential, so the normal probability plot is not a straight\n",
    "line. But with `n=10` the distribution of the sum is approximately\n",
    "normal, and with `n=100` it is all but indistinguishable from normal.\n",
    "\n",
    "Figure [\\[normal1\\]](#normal1){reference-type=\"ref\" reference=\"normal1\"}\n",
    "(bottom row) shows similar results for a lognormal distribution.\n",
    "Lognormal distributions are generally more skewed than exponential\n",
    "distributions, so the distribution of sums takes longer to converge.\n",
    "With `n=10` the normal probability plot is nowhere near straight, but\n",
    "with `n=100` it is approximately normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "3f2234ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeLognormalSamples(mu=1.0, sigma=1.0, iters=1000):\n",
    "    \"\"\"Generates samples from a lognormal distribution.\n",
    "\n",
    "    mu: parmeter\n",
    "    sigma: parameter\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(np.random.lognormal(mu, sigma, n)) for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7a807d6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1600x1000 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeLognormalSamples()\n",
    "NormalPlotSamples(samples, ylabel=\"sum of lognormal values\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "7f98ab93",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeParetoSamples(alpha=1.0, iters=1000):\n",
    "    \"\"\"Generates samples from a Pareto distribution.\n",
    "\n",
    "    alpha: parameter\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(np.random.pareto(alpha, n)) for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "5a039a30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1600x1000 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeParetoSamples()\n",
    "NormalPlotSamples(samples, ylabel=\"sum of Pareto values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cec0afd",
   "metadata": {},
   "source": [
    "Pareto distributions are even more skewed than lognormal. Depending on\n",
    "the parameters, many Pareto distributions do not have finite mean and\n",
    "variance. As a result, the Central Limit Theorem does not apply.\n",
    "Figure [\\[normal2\\]](#normal2){reference-type=\"ref\" reference=\"normal2\"}\n",
    "(top row) shows distributions of sums of Pareto values. Even with\n",
    "`n=100` the normal probability plot is far from straight.\n",
    "\n",
    "I also mentioned that CLT does not apply if the values are correlated.\n",
    "To test that, I generate correlated values from an exponential\n",
    "distribution. The algorithm for generating correlated values is (1)\n",
    "generate correlated normal values, (2) use the normal CDF to transform\n",
    "the values to uniform, and (3) use the inverse exponential CDF to\n",
    "transform the uniform values to exponential.\n",
    "\n",
    "`GenerateCorrelated` returns an iterator of `n` normal values with\n",
    "serial correlation `rho`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "7bf8b9c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def GenerateCorrelated(rho, n):\n",
    "    \"\"\"Generates a sequence of correlated values from a standard normal dist.\n",
    "\n",
    "    rho: coefficient of correlation\n",
    "    n: length of sequence\n",
    "\n",
    "    returns: iterator\n",
    "    \"\"\"\n",
    "    x = random.gauss(0, 1)\n",
    "    yield x\n",
    "\n",
    "    sigma = np.sqrt(1 - rho**2)\n",
    "    for _ in range(n - 1):\n",
    "        x = random.gauss(x * rho, sigma)\n",
    "        yield x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "060814fb",
   "metadata": {},
   "source": [
    "The first value is a standard normal value. Each subsequent value\n",
    "depends on its predecessor: if the previous value is `x`, the mean of\n",
    "the next value is `x*rho`, with variance `1-rho**2`. Note that\n",
    "`random.gauss` takes the standard deviation as the second argument, not\n",
    "variance.\n",
    "\n",
    "`GenerateExpoCorrelated` takes the resulting sequence and transforms it\n",
    "to exponential:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "e0de13ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import expon\n",
    "\n",
    "def GenerateExpoCorrelated(rho, n):\n",
    "    \"\"\"Generates a sequence of correlated values from an exponential dist.\n",
    "\n",
    "    rho: coefficient of correlation\n",
    "    n: length of sequence\n",
    "\n",
    "    returns: NumPy array\n",
    "    \"\"\"\n",
    "    normal = list(GenerateCorrelated(rho, n))\n",
    "    uniform = norm.cdf(normal)\n",
    "    expo = expon.ppf(uniform)\n",
    "    return expo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "9054d1e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeCorrelatedSamples(rho=0.9, iters=1000):\n",
    "    \"\"\"Generates samples from a correlated exponential distribution.\n",
    "\n",
    "    rho: correlation\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(GenerateExpoCorrelated(rho, n)) for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "be3de5f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1600x1000 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeCorrelatedSamples()\n",
    "NormalPlotSamples(samples, ylabel=\"sum of correlated exponential values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e44ca00",
   "metadata": {},
   "source": [
    "`normal` is a list of correlated normal values. `uniform` is a sequence\n",
    "of uniform values between 0 and 1. `expo` is a correlated sequence of\n",
    "exponential values. `ppf` stands for \"percent point function,\" which is\n",
    "another name for the inverse CDF.\n",
    "\n",
    "Figure [\\[normal2\\]](#normal2){reference-type=\"ref\" reference=\"normal2\"}\n",
    "(bottom row) shows distributions of sums of correlated exponential\n",
    "values with `rho=0.9`. The correlation slows the rate of convergence;\n",
    "nevertheless, with `n=100` the normal probability plot is nearly\n",
    "straight. So even though CLT does not strictly apply when the values are\n",
    "correlated, moderate correlations are seldom a problem in practice.\n",
    "\n",
    "These experiments are meant to show how the Central Limit Theorem works,\n",
    "and what happens when it doesn't. Now let's see how we can use it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa118107",
   "metadata": {},
   "source": [
    "## Applying the CLT\n",
    "\n",
    "To see why the Central Limit Theorem is useful, let's get back to the\n",
    "example in Section [\\[testdiff\\]](#testdiff){reference-type=\"ref\"\n",
    "reference=\"testdiff\"}: testing the apparent difference in mean pregnancy\n",
    "length for first babies and others. As we've seen, the apparent\n",
    "difference is about 0.078 weeks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "eb1410e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/2002FemPreg.dct\")\n",
    "download(\n",
    "    \"https://github.com/AllenDowney/ThinkStats2/raw/master/code/2002FemPreg.dat.gz\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "1ee5842d",
   "metadata": {},
   "outputs": [],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/nsfg.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/first.py\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "6564a11c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07803726677754952"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import first\n",
    "\n",
    "live, firsts, others = first.MakeFrames()\n",
    "delta = firsts.prglngth.mean() - others.prglngth.mean()\n",
    "delta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4677bb23",
   "metadata": {},
   "source": [
    "Remember the logic of hypothesis testing: we compute a p-value, which is\n",
    "the probability of the observed difference under the null hypothesis; if\n",
    "it is small, we conclude that the observed difference is unlikely to be\n",
    "due to chance.\n",
    "\n",
    "In this example, the null hypothesis is that the distribution of\n",
    "pregnancy lengths is the same for first babies and others. So we can\n",
    "compute the sampling distribution of the mean like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "759c7700",
   "metadata": {},
   "outputs": [],
   "source": [
    "def SamplingDistMean(data, n):\n",
    "    \"\"\"Computes the sampling distribution of the mean.\n",
    "\n",
    "    data: sequence of values representing the population\n",
    "    n: sample size\n",
    "\n",
    "    returns: Normal object\n",
    "    \"\"\"\n",
    "    mean, var = data.mean(), data.var()\n",
    "    dist = Normal(mean, var)\n",
    "    return dist.Sum(n) / n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "0d436eda",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist1 = SamplingDistMean(live.prglngth, len(firsts))\n",
    "dist2 = SamplingDistMean(live.prglngth, len(others))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "882fd9c6",
   "metadata": {},
   "source": [
    "Both sampling distributions are based on the same population, which is\n",
    "the pool of all live births. `SamplingDistMean` takes this sequence of\n",
    "values and the sample size, and returns a Normal object representing the\n",
    "sampling distribution:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6eb7ae51",
   "metadata": {},
   "source": [
    "`mean` and `var` are the mean and variance of `data`. We approximate the\n",
    "distribution of the data with a normal distribution, `dist`.\n",
    "\n",
    "In this example, the data are not normally distributed, so this\n",
    "approximation is not very good. But then we compute `dist.Sum(n) / n`,\n",
    "which is the sampling distribution of the mean of `n` values. Even if\n",
    "the data are not normally distributed, the sampling distribution of the\n",
    "mean is, by the Central Limit Theorem.\n",
    "\n",
    "Next, we compute the sampling distribution of the difference in the\n",
    "means. The `Normal` class knows how to perform subtraction using\n",
    "Equation 2:"
   ]
  },
  {
   "cell_type": "raw",
   "id": "8f3a2aff",
   "metadata": {},
   "source": [
    "def __sub__(self, other):\n",
    "    return Normal(self.mu - other.mu,\n",
    "                  self.sigma2 + other.sigma2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e712960d",
   "metadata": {},
   "source": [
    "So we can compute the sampling distribution of the difference like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "750e153c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normal(0, 0.00319708)\n"
     ]
    }
   ],
   "source": [
    "dist = dist1 - dist2\n",
    "print(dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f95cd9ca",
   "metadata": {},
   "source": [
    "The mean is 0, which makes sense because we expect two samples from the\n",
    "same distribution to have the same mean, on average. The variance of the\n",
    "sampling distribution is 0.0032.\n",
    "\n",
    "`Normal` provides `Prob`, which evaluates the normal CDF. We can use\n",
    "`Prob` to compute the probability of a difference as large as `delta`\n",
    "under the null hypothesis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "74bf6c31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08377070425543787"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - dist.Prob(delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "558c5533",
   "metadata": {},
   "source": [
    "Which means that the p-value for a one-sided test is 0.084. For a\n",
    "two-sided test we would also compute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "356d9768",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08377070425543781"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist.Prob(-delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7c262b4",
   "metadata": {},
   "source": [
    "Which is the same because the normal distribution is symmetric. The sum\n",
    "of the tails is 0.168, which is consistent with the estimate in\n",
    "Section [\\[testdiff\\]](#testdiff){reference-type=\"ref\"\n",
    "reference=\"testdiff\"}, which was 0.17."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b85a36a5",
   "metadata": {},
   "source": [
    "## Correlation test\n",
    "\n",
    "In Section [\\[corrtest\\]](#corrtest){reference-type=\"ref\"\n",
    "reference=\"corrtest\"} we used a permutation test for the correlation\n",
    "between birth weight and mother's age, and found that it is\n",
    "statistically significant, with p-value less than 0.001.\n",
    "\n",
    "Now we can do the same thing analytically. The method is based on this\n",
    "mathematical result: given two variables that are normally distributed\n",
    "and uncorrelated, if we generate a sample with size $n$, compute\n",
    "Pearson's correlation, $r$, and then compute the transformed correlation\n",
    "$$t = r \\sqrt{\\frac{n-2}{1-r^2}}$$ the distribution of $t$ is Student's\n",
    "t-distribution with parameter $n-2$. The t-distribution is an analytic\n",
    "distribution; the CDF can be computed efficiently using gamma functions.\n",
    "\n",
    "We can use this result to compute the sampling distribution of\n",
    "correlation under the null hypothesis; that is, if we generate\n",
    "uncorrelated sequences of normal values, what is the distribution of\n",
    "their correlation? `StudentCdf` takes the sample size, `n`, and returns\n",
    "the sampling distribution of correlation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "34f8fa6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import t as studentt\n",
    "\n",
    "def StudentCdf(n):\n",
    "    \"\"\"Computes the CDF correlations from uncorrelated variables.\n",
    "\n",
    "    n: sample size\n",
    "\n",
    "    returns: Cdf\n",
    "    \"\"\"\n",
    "    ts = np.linspace(-3, 3, 101)\n",
    "    ps = studentt.cdf(ts, df=n - 2)\n",
    "    rs = ts / np.sqrt(n - 2 + ts**2)\n",
    "    return thinkstats2.Cdf(rs, ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "406e406c",
   "metadata": {},
   "source": [
    "`ts` is a NumPy array of values for $t$, the transformed correlation.\n",
    "`ps` contains the corresponding probabilities, computed using the CDF of\n",
    "the Student's t-distribution implemented in SciPy. The parameter of the\n",
    "t-distribution, `df`, stands for \"degrees of freedom.\" I won't explain\n",
    "that term, but you can read about it at\n",
    "<http://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78aec25e",
   "metadata": {},
   "source": [
    "To get from `ts` to the correlation coefficients, `rs`, we apply the\n",
    "inverse transform, $$r = t / \\sqrt{n - 2 + t^2}$$ The result is the\n",
    "sampling distribution of $r$ under the null hypothesis.\n",
    "Figure [\\[normal4\\]](#normal4){reference-type=\"ref\" reference=\"normal4\"}\n",
    "shows this distribution along with the distribution we generated in\n",
    "Section [\\[corrtest\\]](#corrtest){reference-type=\"ref\"\n",
    "reference=\"corrtest\"} by resampling. They are nearly identical. Although\n",
    "the actual distributions are not normal, Pearson's coefficient of\n",
    "correlation is based on sample means and variances. By the Central Limit\n",
    "Theorem, these moment-based statistics are normally distributed even if\n",
    "the data are not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "bb5ab96a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import hypothesis\n",
    "\n",
    "\n",
    "class CorrelationPermute(hypothesis.CorrelationPermute):\n",
    "    \"\"\"Tests correlations by permutation.\"\"\"\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        \"\"\"Computes the test statistic.\n",
    "\n",
    "        data: tuple of xs and ys\n",
    "        \"\"\"\n",
    "        xs, ys = data\n",
    "        return np.corrcoef(xs, ys)[0][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "4009d34a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ResampleCorrelations(live):\n",
    "    \"\"\"Tests the correlation between birth weight and mother's age.\n",
    "\n",
    "    live: DataFrame for live births\n",
    "\n",
    "    returns: sample size, observed correlation, CDF of resampled correlations\n",
    "    \"\"\"\n",
    "    live2 = live.dropna(subset=[\"agepreg\", \"totalwgt_lb\"])\n",
    "    data = live2.agepreg.values, live2.totalwgt_lb.values\n",
    "    ht = CorrelationPermute(data)\n",
    "    p_value = ht.PValue()\n",
    "    return len(live2), ht.actual, ht.test_cdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "4541a0be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAGwCAYAAABVdURTAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy80BEi2AAAACXBIWXMAAA9hAAAPYQGoP6dpAABTtUlEQVR4nO3dd3gU5doG8Hu276ZTkpCQANJERarEgIhKFBSwohxUmhRBrIhSpFljA+EAioI0GwifwvGAWIKoQOgC4UDoIb1Csmnb5/sjZmFMAmmbye7ev+vaS/bZmd1nsya5887M+wqiKIogIiIi8hAKuRsgIiIiqk8MN0RERORRGG6IiIjIozDcEBERkUdhuCEiIiKPwnBDREREHoXhhoiIiDyKSu4GGprD4UB6ejr8/PwgCILc7RAREVE1iKKIwsJChIWFQaG4+tiM14Wb9PR0REREyN0GERER1UJKSgpatmx51W28Ltz4+fkBKPvi+Pv7y9wNERERVYfRaERERITz9/jVeF24KT8U5e/vz3BDRETkZqpzSglPKCYiIiKPwnBDREREHoXhhoiIiDwKww0RERF5FIYbIiIi8igMN0RERORRGG6IiIjIozDcEBERkUdhuCEiIiKPwnBDREREHkXWcPPHH39gyJAhCAsLgyAI2LRp0zX32bFjB7p37w6tVot27dph9erVLu+TiIiI3Ies4aa4uBhdunTB0qVLq7X9+fPnMWjQINx55504fPgwXnzxRYwbNw4//fSTizslIiKiqykuNSMl85LzlplrlK0XWRfOvPfee3HvvfdWe/tly5ahTZs2mD9/PgCgU6dO2LlzJz766CMMGDDAVW0SEREBAKxWG9KzL8Fud8But8Fut8Nud8DhsMNut8PhEGF32HH6Qg5OXcjBnqMXENLEF4IAiKLovAGARqOBnwct4JyScVFyP7JFE3w0/TFZenGrVcHj4+MRExMjqQ0YMAAvvvhilfuYzWaYzWbnfaNRviRJRESNi81mg8Vicd5yLxpRWFwKq9UKm82GE+ezcKmgBAJEHEzMQM6lkhq/RlKaqdK6VquBX7Gtrm+BKuFW4SYzMxMhISGSWkhICIxGI0pLS6HX6yvsExsbi9dff72hWiQiokbC4XAgMycfxSUlOHE2HSkZF+Fw2GC1WGG1WXE2JQ8nL1xEi6Y+sDkcyLlU2qD9lY/geCp/X51sr+1W4aY2ZsyYgSlTpjjvG41GREREyNgRERHVh1KTBcZiE0RRxNkLWdj112ns2HcKoU19kJ5dALPFCofj2gEiI6+4AbqtyJOzjQDg3r43yfb6bhVuQkNDkZWVJallZWXB39+/0lEbANBqtdBqtQ3RHhERuVDupSL8ceAUbDYb1m7eA5ut7NBR+bku5c4W1/zQUW0JggBBKP9v2Q0QJPWw5v7odn0YWjTzh6BQQCEIEBQKaDQaBAQENFivDUUQBLSLbI6QpvKdT+RW4SY6Ohpbt26V1H755RdER0fL1BEREbmKxWrDhfQ87PnrDL7Zuh82mxVWa/VGY2pKoRAgCAooFAIUCgUEoeJ/e9wQCYVCgeJSC54edjtahTX9O8xU7nLYoYYma7gpKirCmTNnnPfPnz+Pw4cPo0mTJoiMjMSMGTOQlpaGtWvXAgAmTpyIJUuW4NVXX8VTTz2F7du349tvv8WWLVvkegtERFTPUjPy8PS8L2G1WmG1WuocZgQBUCgUUCqVUCgU6Nw+DFqNGkqVCkqlEpl5hXjgzq7Q69QQBKBtZDBCmvg591cqFQwpbkbWcHPgwAHceeedzvvl58aMGjUKq1evRkZGBpKTk52Pt2nTBlu2bMFLL72ERYsWoWXLllixYgUvAycicmOiKKKkpASpaRn4ZP2f+CsxvVbPIwgCVColggJ8cEfPdogIawY/XwO6dWoNg14DpUIBpZIT83sDQfT007X/wWg0IiAgAAUFBfD3oPkFiIjcTWlpKbKyspCdnY2SkhJs3H4SCWdzq7Vv8yAD/Hz0aBPRHE891Bu+vr7wMeihVrvV2RZUAzX5/c3/C4iIqMHYbDZkZ2cjIyMDhYWFZaM2Jhs2bD+J8+kFVe6nUCig12kQE309xg29HX5+vjxURFViuCEiIpczGo1IT09HdnY2HA4HLFY79hxLR9yB5Eq3FwQBarUanTuEY/akwQgK5Eg7VR/DDRERuYTD4UBubi5SU1Ods8MXm6x4/4t9lW6vUCig0aih0WigVqvxydwnZL2cmNwXww0REdUru92OzMxMJCcnS5a/sdocFYKNQiFAo9FCq9VApSq7WgkAbr25DYMN1RrDDRER1Qu73Y709HSkpKTAYrFAFEVYrA5Y7XYs3fgXSkxl6ygJAqBWa6DTaaFWa/DPU2feeO5+3NguTIZ3QJ6C4YaIiOrE4XAgMzMTp8+cxfFz2TCZbfjjcCouGqULRioUCuj1Omi1WigU0kuyp40biK7Xt4SGVztRPeD/RUREVCulJgvWfP8Hjp44j9xLRci6WPmyB2q1CjqdDhqNpsIVTqvfGQ0/H/kWWCTPxHBDREQ1VlxcjCemfoZLxqrXcVKr1TAY9FCr1ZU+/sHURxhsyCUYboiIqNpsNhuSkpKwfuveKoONRqOGXm+ockK9T+c9iWZBvq5sk7wcww0REVXLxYsXcfLkSRw8noqf9yZVeFylUsFgMECjKRupaRvRHGdTcvDGc/cjuIkfgvwNUKmUDdw1eSOGGyIiuiqr1YqzZ88iIyMD81bsrvC4QqGAj48BTz3SFw4RuL1newRfsfAkUUNjuCEioipdunQJJ06cwNHTGfjm50TJY4IA6PV66PV6vDvlYXRoHSJTl0RSDDdERFSBw+HA+fPnceFCMl7/vOJojVqtgq+vL5RKJR4f3IvBhhoVhhsiIpIoLS3F8ePHcfRkClZv+Z/kMUEQ4ONjgFargyAAYx/pg/tu7yxTp0SVY7ghIiKnvLw8HD9+HF/+eAyJFy5KHlOr1fD19YFSWXZS8LcLJkCpVFT2NESyYrghIiKIoogLFy7g9JlzeGtVvOQxQQAMBgN0Oj0EAXjk7u741309K8wyTNRYMNwQEXk5m82GEydOIDc3t0KwUSqV8PPzhUpV9uvimw/HcYkEavT4fygRkRczmUxISEhAcXExVv43QfKYVquBr68vBEHA6Ad7Y8idN8vUJVHNMNwQEXmpwsJCJCQkwGKxYPnmI0jNLgJQ8TBU7EsP8WoocisMN0REXigvLw//+9//4HA48O7avSg12wAACoUAPz8/53pQGz6awHNryO0w3BAReZmsrCwkJiZCFEUcTMx0BhulUgl/fz/n1VDL5j7BYENuieGGiMiLpKWl4fTp0877//nzLICySfn8/PycYWbqmHvQnEsokJtiuCEi8hIXLlzA+fPnAQDGYjPmf30AAKDVauHr6wNBEAAAn73+JJoGctVucl8MN0REXiApKQlJSUkAAIdDdAYbvV4Hg8EHf+caDL2nO4MNuT2GGyIiD3dlsAHgXCvKYDBAr9c7gw0APHJP9wbujqj+MdwQEXmwCxcuSILNsXO5AAAfn7Jgc6UnBkdxgj7yCPy/mIjIQ6WkpDjPsQGAuP0X8MfhVPj6+kCn00m2/er9sdBp1Q3dIpFLMNwQEXmgjIwMnD171nn/y23/w+mUfPj4VAw2/37tXww25FE4gQERkYfJzc3FyZMnnfd/2ZfkDDZ6vTTY3BnVEeHBgQ3cIZFrceSGiMiD5Ofn4/jx4877h05mYeeRtL/PsZEGm4nDbsfdvW9o6BaJXI7hhojIQxQXFyMhIQEOhwMAsHbrMZxNK4Ber69w8vC8yUPQuUO4HG0SuRzDDRGRB7BYLEhISIDdbseR09n4bkfZLMQ6nRYGg0GyLYMNeTqGGyIiN2e325GQkACTyYQ1W4/hXFoBAECj0cDHx1cyj82APjcy2JDHY7ghInJjoigiMTERhYWFOJ1yyRlsytaKkgabcUNvw719b5KpU6KGw3BDROTGkpKSkJOTAwD4clvZicRKpQJ+fn7OtaIA4KVRMbiteztZeiRqaAw3RERuKicnBxcuXAAA/LS3bLI+hUKAn5+/c3Xv0Q/2xt29O3EeG/IqDDdERG6ouLgYiYmJAICCIjN2H02HIAC+vn5QqZQAgBdH9Effnu3lbJNIFgw3RERuxmaz4dixY7Db7fh+xykcPl12WMpg8IFGc3mEhsGGvBVnKCYiciOiKOLEiRMoLS3FsXO5zmCj02klyyrMmzxErhaJZMdwQ0TkRlJSUpCXlwcA2BBXtsSCSqWCj4+P5MooXu5N3oyHpYiI3ERBQYFzle/c/FIA5ScQ+zqvjIru2hYvj46RrUeixoDhhojIDVitVhw/frzssFRSHtb9UnYysa+vH5TKshOIxw/ti4F9b5SzTaJGgYeliIgaufLzbMxmM+x2hzPYGAx6yQnEA27jIphEAMMNEVGjl5qaiosXLwIA3lgZD6BsBmK9/vKaUTe1D5NM2kfkzRhuiIgasaKiIpw7dw4AsHjDIQDl59n4OU8gNug0eP3Z++VqkajR4Tk3RESNlN1ux/Hjx5GWXYgV/zkKu0MEUHaeTfkMxADwxXtPydUiUaPEcENE1EidO3cOmTmX8OmmI86aXi89z+aLdxlsiP6Jh6WIiBqhixcvIi0tDfO/PuCsqVRKGAx65/2lsx+HQa+Roz2iRo3hhoiokbFarUhMTEReQamzVr5uVPlJw+OG3obQZv5ytUjUqPGwFBFRI3PmzBmUlprw728POWsGg49zQcwls4ajRfMAudojavQYboiIGpHc3FxkZWU5L/kGAI1G7Vw3atXbo+Dvq69qdyICD0sRETUaVqsVp06dQonJ6qwpFAJ8fHwhCMD9d3ZhsCGqBoYbIqJG4uzZs7BYLHjvi33OmsHgA6Wy7Ef1qAej5WqNyK0w3BARNQJ5eXnIzMzE3OW7nDWNRg2tVgsA+HbBBLlaI3I7DDdERDKz2+04deoUUrMLnTVBEODj4wNBAEKb+TtHb4jo2vjdQkQks/PnzyP3YiGWbz7qrPn4GJyrfS+d/bhcrRG5JV4tRUQko8LCQuz96wQ+23Q52KjVKmi1ZVdHffPhOLlaI3Jbso/cLF26FK1bt4ZOp0NUVBT27dt31e0XLlyIjh07Qq/XIyIiAi+99BJMJlMDdUtEVH9EUcSWX+MlwaZssr6yq6MeHdgDGjX/BiWqKVnDzfr16zFlyhTMnTsXhw4dQpcuXTBgwABkZ2dXuv3XX3+N6dOnY+7cuThx4gQ+//xzrF+/HjNnzmzgzomI6u7c+Qv4ZON+SU2vLzscpVAo8K97b5GpMyL3JoiiKMr14lFRUbjllluwZMkSAIDD4UBERASee+45TJ8+vcL2zz77LE6cOIG4uDhn7eWXX8bevXuxc+fOSl/DbDbDbDY77xuNRkRERKCgoAD+/py6nIjkYTabMWDsfFz5I1ipVCIwMAARoU2waOYwGbsjanyMRiMCAgKq9ftbtpEbi8WCgwcPIiYm5nIzCgViYmIQHx9f6T69e/fGwYMHnYeuzp07h61bt+K+++6r8nViY2MREBDgvEVERNTvGyEiqoUnpn6Kf/5t6evrg9t7dmCwIaoj2Q7m5ubmwm63IyQkRFIPCQlBYmJipfs8/vjjyM3NxW233QZRFGGz2TBx4sSrHpaaMWMGpkyZ4rxfPnJDRCSXb/67GzkXCyU1nU6LQH9fvDiyv0xdEXkO2U8orokdO3bgnXfewccff4xDhw7hu+++w5YtW/Dmm29WuY9Wq4W/v7/kRkQkl7SsS1j+7R+SmkIhwGAwYO27Y2TqisizyDZy06xZMyiVSmRlZUnqWVlZCA0NrXSf2bNnY8SIERg3ruzSyM6dO6O4uBgTJkzAa6+9BoXCrbIaEXkZURQxfvZq2O12Sd1gMODzt0bJ1BWR55EtDWg0GvTo0UNycrDD4UBcXByioytfP6WkpKRCgCmf5ErG86KJiKpl58FTKCkpldRUKhWmjx+EJgE+MnVF5HlknUBhypQpGDVqFHr27IlevXph4cKFKC4uxpgxZUOzI0eORHh4OGJjYwEAQ4YMwYIFC9CtWzdERUXhzJkzmD17NoYMGeIMOUREjdWbH/9Q4Q+x/tE3om/P9jJ1ROSZZA03w4YNQ05ODubMmYPMzEx07doV27Ztc55knJycLBmpmTVrFgRBwKxZs5CWlobmzZtjyJAhePvtt+V6C0RE1ZKfny+ZlgIoO4l45sTBMnVE5LlknedGDjW5Tp6IqD6Iooi7x7wPq9XmrAmCgFu6dMAHrwyVsTMi9+EW89wQEXmL9IxMSbABAINBj9mTBsnUEZFnY7ghInIhu92OBau2SWpKpQI6nQ7+vnqZuiLybAw3REQulJKSggPH0yU1Hx8f/N+iiTJ1ROT5GG6IiFzEbDZj2oJNkpparYZarYEgCPI0ReQFGG6IiFxkwcotyMwrltR8fAwYcsfNMnVE5B0YboiIXCAn7xK27Twhqel0WqhUKjw5JEqmroi8A8MNEZELPD51ueS+IAB6vQHL3xgBtZqTjhK5EsMNEVE9e+WDb2GxWCU1vV6POc8M5jILRA2A4YaIqB7lXCzEoWPnJTWFQoBOp0f3GyJl6orIuzDcEBHVozEzV8Jmk07Yp9cbsPbdMTJ1ROR9GG6IiOpJvrEEJSUlkppSqcBnb4yEn49Opq6IvA/DDRFRPXnilc9gtzsktZs6RKBlaBOZOiLyTgw3RET1YH/CeZSUlEpqKpUKi157QqaOiLwXww0RUT2Yu3gTHA7pqI3BoOdMxEQyYLghIqqjld/tRGmpdNRGrVZh46JJMnVE5N0YboiI6mjDj/vgcIiS2tSnBkCrUcvUEZF3Y7ghIqoDs9mM0lKTpKbRqDHw9q7yNEREDDdERHXx686/IIrSUZtxj94uUzdEBDDcEBHVmtVqxQertktqWq0Gj9xzi0wdERHAcENEVGtPvrq8wqiNwWCASsWFMYnkxHBDRFQLazftRlbOJUlNq9VizMO3ydQREZVjuCEiqqEtvyfg6//G48pBG0Eom9fmgbu6yNcYEQFguCEiqhGbzY4VG/+EySS9Qkqr1WLVO1wck6gxYLghIqqBl9/fiNLS0gqjNmMe7osgf4N8jRGRE8MNEVE1HTudhuSMvAqjNk89GIV/DYqSqSsi+ieGGyKiasjMNWLukh9QWmqqMGrz6KA+8jVGRBUw3BARVcPkN7+Gw+GoMGrz0dT7odfrZeqKiCrDcENEdA2Lv/oNAGAymSTz2tzdqxU6dmgrV1tEVAWGGyKia9ix7yQcDodkDak2Yf545J4eMBh4EjFRY8NwQ0R0FRt+Ogig4qjNyHtvQqtWreRqi4iuguGGiOgq1m3dD4dDlJxr8+hdHRAaGsJRG6JGiuGGiKgKCafSAABmswkOx+VRm5vaNueoDVEjxnBDRFSFeUt/gCiKKC0tddaG3NYWzZo1g4+Pj4ydEdHVMNwQEV2FyWSWjNr07BSKyMhIGTsiomthuCEiqkRK5iWIogiT6fKozS03hCIoKAj+/v4ydkZE18JwQ0RUiRdj18NstsBudzhrfbu05Lk2RG6A4YaI6B9Wf78bogjJuTYAEBHWHAEBATJ1RUTVxXBDRHQFURTxw46jsFgssNvtznqHyCC0atUKgiDI2B0RVQfDDRHRFeL2JFY6ajP+oZ5o0qSJTF0RUU0w3BARXeGTdb/DZrPCZrM5a08/2IWjNkRuhOGGiOhvxaVmABVHba6LaIbg4GA5WiKiWmC4ISL628R5X8Fms8FisTprA29tg4iICI7aELkRhhsiIpSdSFxislQYtbm9eyuEhobK1BUR1QbDDRERgDWb4mG322GxWCT18PBwKJVKmboiotpguCEir1dcasYPO46itNQE8fJKC5gx6laEh4fL1xgR1QrDDRF5vZHTV8HhcMBsNknq7a5rBbVaLVNXRFRbDDdERChbIPPKUZux99+Mli1bytcQEdUaww0RebW8/KIKC2QCwC03t4NOp5OpKyKqC4YbIvJqE+Z+CbPZDIfj8rDN0w92QUREhIxdEVFdMNwQkVerbKmFG9q3hK+vr0wdEVFdMdwQkdfKyCmA1WqB3e5w1sKb+yIyMlLGroiorhhuiMhrPfvWNxVGbUYN6YagoCCZOiKi+sBwQ0ReKS+/CFarDVarTVLvelNHLrVA5OYYbojIK02Y+2WFK6R89Bo0b95cpo6IqL4w3BCR1/n+179gt9thNkuXWlg2ZxgUCv5YJHJ3/C4mIq9yyViCL3/YC5NJOhtxeHNfhIWFydQVEdUn2cPN0qVL0bp1a+h0OkRFRWHfvn1X3T4/Px+TJ09GixYtoNVq0aFDB2zdurWBuiUid3fo+AU4HCJMJrOk/sazg6BSqWTqiojqk6zfyevXr8eUKVOwbNkyREVFYeHChRgwYABOnjyJ4ODgCttbLBbcfffdCA4OxsaNGxEeHo4LFy4gMDCw4ZsnIre0fMNOmM0miFestfD4PZ24QCaRB5E13CxYsADjx4/HmDFjAADLli3Dli1bsHLlSkyfPr3C9itXrsTFixexe/du52J2rVu3vuprmM1mmM2X/0IzGo319waIyK3YbHZYrDaUlkoPSd3WsyP0er1MXRFRfZPtsJTFYsHBgwcRExNzuRmFAjExMYiPj690n//85z+Ijo7G5MmTERISgptuugnvvPMO7HZ7la8TGxuLgIAA541TqhN5r7c//REWiwUOh0NS588FIs8iW7jJzc2F3W5HSEiIpB4SEoLMzMxK9zl37hw2btwIu92OrVu3Yvbs2Zg/fz7eeuutKl9nxowZKCgocN5SUlLq9X0QkXsQRRFHTqZWGLWZNa4f/P39ZeqKiFzBrc6eczgcCA4OxmeffQalUokePXogLS0NH3zwAebOnVvpPlqtFlqttoE7JaLGJudSEWw2K2y2ipP2EZFnkS3cNGvWDEqlEllZWZJ6VlYWQkNDK92nRYsWUKvVUCqVzlqnTp2QmZkJi8UCjUbj0p6JyH2lZeVXGLWZOaYPmjVrJlNHROQqsh2W0mg06NGjB+Li4pw1h8OBuLg4REdHV7pPnz59cObMGcnx8lOnTqFFixYMNkR0VSfPpcNikU7ad0PHtlxqgcgDyTrPzZQpU7B8+XKsWbMGJ06cwKRJk1BcXOy8emrkyJGYMWOGc/tJkybh4sWLeOGFF3Dq1Cls2bIF77zzDiZPnizXWyAiN7Hm+12S+4IgoEWLFjJ1Q0SuJOs5N8OGDUNOTg7mzJmDzMxMdO3aFdu2bXOeZJycnCyZCj0iIgI//fQTXnrpJdx8880IDw/HCy+8gGnTpsn1FojIDdhsNpT+Y0ZinU7LSfuIPJQgXjmTlRcwGo0ICAhAQUEBr5Ag8hJHjp3E87EbJbWmTYLw3eJnZOqIiGqqJr+/ZV9+gYjIlURRxLyPt0hqGo0GMycOkqkjInI1hhsi8mh5eXm4WFAqqen1OvS4IVKmjojI1RhuiMijbf5FuhivSqWESqXmVVJEHozhhog8VlFREdb+9y9JTa/X45Wn7pGpIyJqCAw3ROSxUlNTJfcVCgEajQa3dmkjU0dE1BAYbojII1ksFmyOk47a6HQ6xER34iEpIg/HcENEHik9PR1bd59z3heEsnBz/11dZOyKiBoCww0ReRyHw4FdB45LalqtFgqFAi1DgmTqiogaCsMNEXmc7OxsrNhc8ZDUa0/fJ1NHRNSQGG6IyKOIooiUlBRcsb4u1GoVVCoVunNuGyKvwHBDRB7FaDRi6sKfJTW9Xo/be7aXqSMiamgMN0TkUZKSLkjuK5UKqNUajHwgWqaOiKihMdwQkccwmUz43+lkSU2n00EQgCB/g0xdEVFDY7ghIo+Rnp6OT78/4rwvCAK0Wh02fDRBxq6IqKEx3BCRR7Db7UhLS5PUyi7/FqBQ8EcdkTep0Xf8yJEjUVhY6Lx/5MgRWK3Wem+KiKimsrKyMGvZH5KaXq/j4SgiL1SjcPPVV1+htLTUeb9v375ISUmp96aIiGqi7PJv6TpSGo0aSqUS8199VKauiEguNQo3oihe9T4RkRzy8/Px697TkppOpwMABPjp5WiJiGTEA9FE5PZSU1Ox88jlkRulUgm1WoNvF/BEYiJvpKrpDsePH0dmZiaAspGbxMREFBUVSba5+eab66c7IqJrKC0tRV5eHkpMNmet/PJvpZJ/vxF5oxqHm/79+0sORw0ePBhA2SWXoihCEATY7fb665CI6CrS0tJQWGxx3lcoBOh0Wgy5g39kEXmrGoWb8+fPu6oPIqIas9lsyMjIwJnUS86aVquFIAh45J7uMnZGRHKqUbhp1aqVq/ogIqqxrKws2O12bPrjjLNWfiKxn49OrraISGY1PiwFAKdPn8bmzZuRlJQEQRDQpk0bPPjgg7juuuvquz8iokqJoojU1FRsP3h5uQWNRgOlUiljV0TUGNQ43MTGxmLOnDlwOBwIDg6GKIrIycnB9OnT8c4772Dq1Kmu6JOISOLixYsoKSnB74cuz7VVPmpzZ1RHudoiokagRpcS/Pbbb5g1axZee+015ObmIiMjA5mZmc5wM336dPzxxx/XfiIiojpKS0vD//12ynlfpVJCrVYDAJ5+9Ha52iKiRkAQazAT37BhwxAYGIhPP/200scnTJiAwsJCfPPNN/XWYH0zGo0ICAhAQUEB/P395W6HiGqhpKQEs+Z/jYOJWc6ar68PdDodFkx7FK3CmsrYHRG5Qk1+f9do5Gbfvn0YMWJElY+PGDECe/bsqclTEhHVWHJKiiTYKBQCtFotADDYEFHNwk1WVhZat25d5eNt2rRxTvBHROQKNpsNn23YKalptToIgoDZkwbJ1BURNSY1CjcmkwkajabKx9VqNSwWS5WPExHVVUZGBg6euPxHlCAAOp0WsycNQtfrI2TsjIgaixpfLbVixQr4+vpW+lhhYWGdGyIiqoooijiflCyplV/+zWBDROVqFG4iIyOxfPnya25DROQKeXl5WP79QUlNp9PhpvZhMnVERI1RjcJNUlKSi9ogIrq2tLQ0JGddHiFWqZRQqdR46uE+MnZFRI1Njc652b59O2644QYYjcYKjxUUFODGG2/En3/+WW/NERGVKy4uRnJalqSm0+khCLxCioikahRuFi5ciPHjx1d6fXlAQACefvppLFiwoN6aIyIql5qaiiUbDznvl13+rcG8yUNk7IqIGqMahZsjR45g4MCBVT5+zz334ODBg1U+TkRUG1arFVlZWTCZ7c6aTld2+TfPtyGif6rxPDfl05tXRqVSIScnp85NERFdKSMjA1arzXlfEMrmtin7tyBXW0TUSNUo3ISHh+PYsWNVPn706FG0aNGizk0REZUTRRFpaWl4Y2W8s1Z2+bcCTz/GNaSIqKIahZv77rsPs2fPhslkqvBYaWkp5s6di8GDB9dbc0REOTk5+HXvWUlNp9MDAG7r3k6OloiokavRpeCzZs3Cd999hw4dOuDZZ59Fx44dAQCJiYlYunQp7HY7XnvtNZc0SkTeKS0tDb/uv+C8r1aroFaX/egy6KueMZ2IvFeNwk1ISAh2796NSZMmYcaMGShfUFwQBAwYMABLly5FSEiISxolIu9TWFiIrX8el9R0urJzbTYufFqOlojIDdR4+YVWrVph69atuHTpEs6cOQNRFNG+fXsEBQW5oj8i8mKpqan4eW+S875CIUCj0WD6+IE8kZiIqlTjcFMuKCgIt9xyS332QkTkZLFYcPpciqRWNmmfgFtuai1PU0TkFmp0QjERUUNJS0vD/K/3O++Xr/790qgYGbsiInfAcENEjY7D4UB6erqkptVqoVAo0KdbW5m6IiJ3wXBDRI1OdnY2jpzKkNTKTyTmuTZEdC0MN0TUqIiiiNTUVKz/9aSzplaroFKpsGjmMBk7IyJ3wXBDRI1KQUEBcvLyJTW9vmzSvpYhvCqTiK6N4YaIGpXU1FTs/d/lQ1JKpQJqtQZznuHs50RUPQw3RNRolJaWIisrG78dTHbWylb/Brp0bCljZ0TkThhuiKjR+OcCmYIgOFf/JiKqLoYbImoUbDYbLiSnSmo6nRYKhYB5k4fI1BURuSOGGyJqFDIyMrD+18rXkercIVyOlojITTHcEJHsRFFE0oVknLxwyVnTaDRQKpXY8NEEGTsjInfEcENEssvNzcWB/0kPSen1ZaM2CgV/TBFRzfCnBhHJLjU1FZv+OOO8r1KpoFKpsWDaozJ2RUTuqlGEm6VLl6J169bQ6XSIiorCvn37qrXfunXrIAgCHnzwQdc2SEQuU1hYiIuX8iU1vb7s8u9WYU3laYqI3Jrs4Wb9+vWYMmUK5s6di0OHDqFLly4YMGAAsrOzr7pfUlISpk6dir59+zZQp0TkCsnJyXjj893O+wqFAI1Gw5OIiajWZA83CxYswPjx4zFmzBjccMMNWLZsGQwGA1auXFnlPna7HU888QRef/11XHfddQ3YLRHVJ5PJhN/3JUpqOp0egiBgzqRBMnVFRO5O1nBjsVhw8OBBxMTEOGsKhQIxMTGIj4+vcr833ngDwcHBGDt27DVfw2w2w2g0Sm5E1DikpaVh/a+Xw40glM1tA/BEYiKqPVl/euTm5sJutyMkJERSDwkJQWZmZqX77Ny5E59//jmWL19erdeIjY1FQECA8xYREVHnvomo7mw2G/YfOSmpabU6KBQKbFz4tExdEZEncKs/jQoLCzFixAgsX74czZo1q9Y+M2bMQEFBgfOWkpLi4i6JqDoyMzORkVsoqen1Ojz1cB8IgiBTV0TkCVRyvnizZs2gVCqRlZUlqWdlZSE0NLTC9mfPnkVSUhKGDLk8FbvD4QBQdunoyZMn0bZtW8k+Wq0WWq3WBd0TUW2JoojU1FTsOXZ59e/ySfsG9essY2dE5AlkHbnRaDTo0aMH4uLinDWHw4G4uDhER0dX2P76669HQkICDh8+7Lzdf//9uPPOO3H48GEeciJyE7m5uTCZTMjMK3bW9HodWjQPkLErIvIUso7cAMCUKVMwatQo9OzZE7169cLChQtRXFyMMWPGAABGjhyJ8PBwxMbGQqfT4aabbpLsHxgYCAAV6kTUeKWkpKC41Oq8Xz5pX0ZOgYxdEZGnkD3cDBs2DDk5OZgzZw4yMzPRtWtXbNu2zXmScXJyMq+aIPIgBQUFMBqNSM2+fL5N+aR97015WMbOiMhTCKIoinI30ZCMRiMCAgJQUFAAf39/udsh8jrHjh1Dbm4u5i7fBaDsku+goCAIAvB/iybK3B0RNVY1+f3NIREiajAlJSXIzc3FlX9TlY/aEBHVF4YbImow5VMxnEsvO7dGoRCg1erkbImIPBDDDRE1CIvF4pz2Ye3W/wEon7SvbNjmmw/HydYbEXkWhhsiahBpaWlwOBxY+2NZsClbauHyqI1GLfv1DUTkIRhuiMjl7HY70tLSYLM7cDY1H0DZBJtKZdmPoDDOb0NE9YjhhohcLjMzEzabDW+uvLwgrk6nd/779eful6MtIvJQHAcmIpcSRREpKSmSK6Q0GjVUKiUAYMWbIxHkb5CrPSLyQBy5ISKXys7Ohslkwgdf7XfW9PrLozYMNkRU3xhuiMhlykdtTiZfdC63oFaXLbUAAGvfHSNne0TkoRhuiMhlLl26hKKiInz90wlnTafTOyft89FrZeqMiDwZww0RuUxycjIsVrvzvlKphEajAQB8NP0xudoiIg/HcENELmE0GpGfn48PJefalC210P/W6xHZoomM3RGRJ2O4ISKXSE5OBgCY/x65KVtqoeww1IRH+8rWFxF5PoYbIqp3xcXFyM3NRWp2obOm1+sh/H2yTfll4ERErsBwQ0T1rnyBzO93nAYgXSBzxZsjZeuLiLwDww0R1SuTyeRcIDO3oBRA2RpS5Qtkcl4bInI1zlBMRPUqJSUFDocDH607AEC6QGbTQB85WyMiL8FwQ0T1xmKxICMjA/NW7HbWykZtygaJp40dKFdrRORFeFiKiOpNSkoK7PbL89qUjdpcXmqhbWRzOdoiIi/DcENE9cJqtSI9PR1Hz+Q4a1qtFkpl2Y+ZN59/QK7WiMjL8LAUEdWLtLQ0GItM+O7vK6SAywtkfjrvSTQL8pWrNSLyMhy5IaI6s9lsSE1Nxftf7nPWtFoNlMqy+WwYbIioITHcEFGdpaWl4WzqRUlNry+75Puph/vI0RIReTGGGyKqE5vNhpSUFGzcftJZ02o1zlmIB/XrLFdrROSlGG6IqE7S09Nhs9lgLLY4a+Xn2qz7cLxcbRGRF2O4IaJas9vtSElJwbFzuc6aRqOGSlV2rYJazTWkiKjhMdwQUa2lp6fDarViQ9zlQ1IGA8+1ISJ5MdwQUa2Uj9p89dNxZ+3KUZsBfW6QqzUi8nIMN0RUK+np6Yg/moxTyZectfIrpB4d2MN5QjERUUPjJH5EVGN2ux3vf74NR09nO2sajRpqddmPlH/de4tcrRERceSGiGrui+9/lwQb4PKozSdzn5CjJSIiJ4YbIqoRm82GNZv3SGrlozYP9e+K4CZ+MnVGRFSGh6WIqEZ++v0gHA5RUjMYDHj28TtxZ1RHmboiIrqM4YaIqs1YVIIPV8dJahqNBu+89DBubBcmU1dERFI8LEVE1fbGku8rGbXRM9gQUaPCcENE1ZKZcwkHjl2Q1DQaDSY/fpdMHRERVY7hhoiqZfSMlRDFiufa3MPJ+oiokWG4IaJrKioqhslkktS0Wi3WvDtGpo6IiKrGcENE17RtxwFcOWgjCEDTJgEI9DPI1xQRURUYbojoqi5eKsCSdTslNa1Wh68/GCdTR0REV8dwQ0RX9a+XP6swamMw6CEIgnxNERFdBcMNEVXJaDTCbLZIajqdHjfw0m8iasQYboioUqIo4uHnP5HUFAoBer0Obzx7v0xdERFdG8MNEVXqgxVbYLXaJDW9Xo/V74yBUskfHUTUePEnFBFVYLfbse3PY5KaUqmATqdDgJ9epq6IiKqH4YaIKnjl/fWw2+2SmsFgwLr542XqiIio+hhuiEjCYrHir+NJkppKpcSy10dCo+Zau0TU+DHcEJHEA5MXV7I4pg9ahgTJ1BERUc0w3BCR07+/+BWlpaWSmkajxuJZw2XqiIio5hhuiMjpv7/9VcmEfT5oHd5MvqaIiGqI4YaIAAAjpq2oMGGfVqvDpiXPyNQREVHtMNwQEfLyi5CemSepKRQCVsc+xWUWiMjtMNwQEUZO+xw2W8UJ+1oE8yRiInI/DDdEXs5ms6GkpFhSUyqV+PztMTJ1RERUNww3RF5u8MRFFS79DmkehBbNA+VpiIiojhhuiLxYdu4lmEwmSU2jUWPtu2Nl6oiIqO4aRbhZunQpWrduDZ1Oh6ioKOzbt6/KbZcvX46+ffsiKCgIQUFBiImJuer2RFQ5URTx+NTPKlz67ePjAzVnIiYiNyZ7uFm/fj2mTJmCuXPn4tChQ+jSpQsGDBiA7OzsSrffsWMHhg8fjt9++w3x8fGIiIjAPffcg7S0tAbunMi9HUo4Vemq3+sXTJCpIyKi+iGIoiheezPXiYqKwi233IIlS5YAABwOByIiIvDcc89h+vTp19zfbrcjKCgIS5YswciRI6+5vdFoREBAAAoKCuDv71/n/onc0Zbfj+LDFf+VnGujVCrQvk1LfPr6CBk7IyKqXE1+f8s6cmOxWHDw4EHExMQ4awqFAjExMYiPj6/Wc5SUlMBqtaJJkyaVPm42m2E0GiU3Im8miiL+vfaXCicR+/j4MNgQkUeQNdzk5ubCbrcjJCREUg8JCUFmZma1nmPatGkICwuTBKQrxcbGIiAgwHmLiIioc99E7spud+CByUsrPYn4xvYtZeqKiKh+yX7OTV28++67WLduHb7//nvodLpKt5kxYwYKCgqct5SUlAbukqjxeHf5jyguLpLUBAHo0CYcsS89JFNXRET1S9ZLIpo1awalUomsrCxJPSsrC6GhoVfd98MPP8S7776LX3/9FTfffHOV22m1Wmi12nrpl8jd7Tp0CjabXVIzGAxYOucJmToiIqp/so7caDQa9OjRA3Fxcc6aw+FAXFwcoqOjq9zv/fffx5tvvolt27ahZ8+eDdEqkdu7mG9ESUmJpKZSKfHDJ8/L1BERkWvIPpnFlClTMGrUKPTs2RO9evXCwoULUVxcjDFjyqZ+HzlyJMLDwxEbGwsAeO+99zBnzhx8/fXXaN26tfPcHF9fX/j6+sr2PogaM1EU8diLn+Cf10aOe/R2KJVKeZoiInIR2cPNsGHDkJOTgzlz5iAzMxNdu3bFtm3bnCcZJycnQ6G4PMD0ySefwGKxYOjQoZLnmTt3LubNm9eQrRO5jRff/qrCnDY6nQ5DB0TJ1BERkevIPs9NQ+M8N+RtziZnYuzMlbjyW12hUCAwMBDfL54kY2dERNXnNvPcEJFrORwOPD1nLf75N4yvrw+++/dEmboiInIthhsiDzZk0r9htVolNZ1Oi/ULJkIQBJm6IiJyLYYbIg9VUlKC4mLp1VEKhQJjh/aDQa+RqSsiItdjuCHyQKIoYub89ZUejnrs3ltk6oqIqGEw3BB5oG//+yf+SkyX1HQ6Lda+N06mjoiIGo7sl4ITUf0aM2MlzqdkSGpKpQI+Pj4I8jfI1BURUcPhyA2RB/nul0O4kJYlmaxPEABfXz+seHOkfI0RETUghhsiD/Lpuu2w2x2Sml6vx+A7uqBJgI9MXRERNSweliLyECmpaTCZzJKaWq3CvOceQtTNbWTqioio4XHkhsgDFBcXY8T01ZKaIAgY+2g/Bhsi8joMN0Ruzm63Y87CDRUWxfT19cHDd/eQpykiIhkx3BC5MVEU8d9fduPA8TRJXafTIsDfF1qNWqbOiIjkw3BD5MZSUtOw4Is/JDWVSgkfHx98Ou9JmboiIpIXww2Rm8rPz8fIGWskNUEQ4Ofnh8WzhsPXoJWpMyIieTHcELkhs9mMFet+rvQ8m2H39UJ4cKAsfRERNQYMN0RuxuFwYOX6n/HDn6cldb1eD61Wi+H3ce0oIvJuDDdEbkQURZw8eRLrfjoqqavVahgMBmxc+LRMnRERNR4MN0RuJDk5GT/tTJDUlEoF/Px8MXfyYAiCIFNnRESNB8MNkZvIysrCuXPn8P2Oy4ejyk8gfiimG7p0bCljd0REjQeXXyByAwUFBfjvr3uwdusxSd3PzxcqlQojH4iWqTMiosaH4YaokSsuLsZr89cj4WyOpO7jY4BGo8HA226UqTMiosaJ4YaoEUs4mYzn3/oKDod0pW+dTgedTg8AGPUgR22IiK7EcEPUCNlsdny6/nf83097KwQbjUYNHx8fCAIw/9Wh0Kj5bUxEdCX+VCRqZIpLzXjy1ZUwGo2w26XBRq1Wwc/PD0893BuD77hZpg6JGje73Q6r1Sp3G1QLGo0GCkXdr3ViuCFqZDbHHUZhoRE2m01SV6mU8PPzw79f+xdahgTJ1B1R4yWKIjIzM5Gfny93K1RLCoUCbdq0gUajqdPzMNwQNSI2mw0rN+6A1SoNNkqlAr27X483nn+Ac9kQVaE82AQHB8NgMPB7xc04HA6kp6cjIyMDkZGRdfr8GG6IGgm73Y7fd+6rEGwUCgEfvjoM3W+6TqbOiBo/u93uDDZNmzaVux2qpebNmyM9PR02mw1qtbrWz8NJ/IgaAavViiNHjuCN5b9J6gqFgNefe4jBhugays+xMRgMMndCdVF+OMput9fpeThyQySj4lIzDh5LQsL/TiA9O1/ymEIhwN8/ALf36iRPc0RuiIei3Ft9fX4MN0QyMVusGDNzNXLzLla4Kqo82HRoEypTd0RE7ouHpYhkMmLaSuTk5lUZbFQqJWJffFCe5ojII91xxx148cUX5W7D5RhuiGSw7r+7kZ2TB4dDlNSVSgUCAsqCze0920OlUsrUIRE1hJycHEyaNAmRkZHQarUIDQ3FgAEDsGvXLuc2giBg06ZN8jV5DaNHj8aDDz54ze0aMljxsBRRA9v442588s1vFeoqlRLdb2qLpPRLePqxvuh/6/UydEfk/kRRlH0SP7VaXa3zRx555BFYLBasWbMG1113HbKyshAXF4e8vLwG6NJzMdwQNRCHw4H//Lwbi7/8vcJjarUK6z96Bk2D/GTojMizWK1W7N69W9Yeevfufc2J6PLz8/Hnn39ix44d6NevHwCgVatW6NWrl3Ob1q1bAwAeeugh5+NJSUkYPXo08vPzJSM6L774Ig4fPowdO3YAKFt0d9KkSfjuu+/g5+eHqVOnVujBbDbjtddewzfffIP8/HzcdNNNeO+993DHHXcAAFavXo0XX3wR69evx4svvoiUlBTcdtttWLVqFVq0aIF58+ZhzZo1AC6fDPzbb7859y83evRo/P777/j999+xaNEiAMD58+ed76++8bAUUQMwm80YM/1TfPRFxWCj1Wox59mHGGyIvIyvry98fX2xadMmmM3mSrfZv38/AGDVqlXIyMhw3q+OV155Bb///js2b96Mn3/+GTt27MChQ4ck2zz77LOIj4/HunXrcPToUTz66KMYOHAgTp8+7dympKQEH374Ib744gv88ccfSE5OdgalqVOn4rHHHsPAgQORkZGBjIwM9O7du0IvixYtQnR0NMaPH+/cLiIiotrvpaY4ckPkYvn5+Yj7Yy+S0i5WeMxg0GPyEzG4vWcHGTojIjmpVCqsXr0a48ePx7Jly9C9e3f069cP//rXv3DzzWVrxzVv3hwAEBgYiNDQ6l89WVRUhM8//xxffvkl+vfvDwBYs2YNWrZs6dwmOTkZq1atQnJyMsLCwgCUhZVt27Zh1apVeOeddwCUjYQtW7YMbdu2BVAWiN544w0AZQFNr9fDbDZftb+AgABoNBoYDIYavY/aYrghcpGsPCPW/N8ObPk9ocJjglD2Q6F500AugEnkxR555BEMGjQIf/75J/bs2YMff/wR77//PlasWIHRo0fX+nnPnj0Li8WCqKgoZ61Jkybo2LGj835CQgLsdjs6dJD+cWU2myWzPBsMBmewAYAWLVogOzu71r01BIYbonpks9nxwcqfsffoORQVFVVYSgEouyLKz88Pz4/oj/63coI+ovqmVqsrPTTS0D1Ul06nw9133427774bs2fPxrhx4zB37tyrhhuFQgFRlF5tWdOTqIuKiqBUKnHw4EEoldIrM319fZ3//ud7EQShwms3Ngw3RPUkv7AET722FmazCSUlJRUu8wYAjUYNX19fPDP8DgYbIhcRBKHOq0rL6YYbbpCcKKxWqyssR9C8eXMcO3ZMUjt8+LAziLRt2xZqtRp79+5FZGQkAODSpUs4deqU8+Tlbt26wW63Izs7G3379q11vxqNplrLJVR3u/rAE4qJ6kgURRw6nozRM1bBaDSiqKi4QrARhLKhXT8/f7QMCcLdvW+QqVsiaizy8vJw11134csvv8TRo0dx/vx5bNiwAe+//z4eeOAB53atW7dGXFwcMjMzcenSJQDAXXfdhQMHDmDt2rU4ffo05s6dKwk7vr6+GDt2LF555RVs374dx44dw+jRo6FQXP6136FDBzzxxBMYOXIkvvvuO5w/fx779u1DbGwstmzZUu330bp1axw9ehQnT55Ebm5ulSNIrVu3xt69e5GUlITc3Fw4HI5Kt6sPHLkhqqWLBcX4+JsdOHQ8BSZTKUpKSisdqlUqFfD19cOT99+KB+7qAq2m9ivdEpHn8PX1RVRUFD766COcPXsWVqsVERERGD9+PGbOnOncbv78+ZgyZQqWL1+O8PBwJCUlYcCAAZg9ezZeffVVmEwmPPXUUxg5ciQSEi6f4/fBBx+gqKgIQ4YMgZ+fH15++WUUFBRIeli1ahXeeustvPzyy0hLS0OzZs1w6623YvDgwdV+H+PHj8eOHTvQs2dPFBUVVXopOFB2svKoUaNwww03oLS01KWXggtiYz9wVs+MRiMCAgJQUFAAf39/udshN/Xy+xuRlFb2F0pxcTFstsqHWt945h70ieoGlYp/RxC5kslkwvnz59GmTRvodDq526FautrnWJPf3/yJS1RNCafS8MNvR3Hw+AXY7XaUlJRWOTeFSqXE+vnj0KxZswbukoiIGG6IrsJud2DN5njn5dwOhwOlpaUwmUyoasxzcL8b8dJTgzlaQ0QkE/70JaqCsagUY14rm1bc4XDAZDLBZDJVehWUj16NQbd1wKODbkNwc47WEBHJieGGqApjXlvz90iN6e+RmsqHaiYP7Y7et3RGeHh4tRbKIyIi12K4Ifpb9sVCxB8+h7Wb42Gz2WEylZ1TU1mm6dy2GXz0Gjx0d3d0v7mTW8+pQUTkaRhuyOuJooihL34KURRhsVhhMpmqnKehd+cw3NkjEi3DW6BNmzbQ6/UN3C0REV0Lww15tR37TuKjNb/CbDbBbDZXej5NudfH90FwcDAiIyMlU5MTEVHjwnBDXic54yKef/sbmM0WWCzmKueoKScIwMTHeqNXr14wGAwN1CUREdUWww15BVEUkZyWhV92JeCbrQevGWgA4JYbWmDg7Tfjli7XI8CfIzVERO6C4YY8kiiKOHoyBW8t+y8KjCWwWi1XPeR0pflTBqJleDiCg4Ml67AQEXmL0aNHIz8/X7KApzthuCGPIIoiSktLkZyWhd/2nMCGX47Abq/+omwKhQJD7+mC0Q/3g4+Pjws7JSIiV2O4IbcjiiJKSkpwPiULRxOTcSopE8fOZCDnUkmNnkehEBAU4IsPXxmKNpEtOEcNkYcQRRHGIpOsPfj76vgzRUYMN9Ro2Ww2mEwmlJaWoqSkBGcuZGLnX+dgtVjw5+HUWj2nUqmARqOBRqPB8yNiEBPdqZ67JiK5GYtMeGrWGll7WPnWKAT4VW+qiI0bN+L111/HmTNnYDAY0K1bN2zevBnHjx/HzJkz8ddff8FqtaJr16746KOP0L17d+e+giBg2bJl+OGHH7B9+3a0atUKK1euRPPmzTFu3Djs378fXbp0wRdffIG2bdsCAObNm4dNmzZh0qRJeOutt5CXl4fBgwdj+fLlCAgIqLRHh8OB9957D5999hkyMzPRoUMHzJ49G0OHDq37F8sFGG5IFg6HAxaLBRaLBWaz2XkrX+LgyrlmLDY7/r3+EApLLDV+HUEQoFarER4ShLFD+6JtZAjCggPr+d0QEdVORkYGhg8fjvfffx8PPfQQCgsL8eeff0IURRQWFmLUqFFYvHgxRFHE/Pnzcd999+H06dPw8/NzPsebb76JBQsWYMGCBZg2bRoef/xxXHfddZgxYwYiIyPx1FNP4dlnn8WPP/7o3OfMmTP49ttv8cMPP8BoNGLs2LF45pln8NVXX1XaZ2xsLL788kssW7YM7du3xx9//IEnn3wSzZs3R79+/Vz+daqpRhFuli5dig8++ACZmZno0qULFi9ejF69elW5/YYNGzB79mwkJSWhffv2eO+993Dfffc1YMfepaCwFAVFpRXqosMBu8MBu90Oh90O2xX/tdtssNpssNtssNntsFmtsNpssFgsOHYmCyazFYJCQH6hCUdO56BZgB6oZAQ3N7/i616NQiFApVJDrVZBrVZj7NC+uP/OLrV960RELpWRkQGbzYaHH34YrVq1AgB07twZAHDXXXdJtv3ss88QGBiI33//HYMHD3bWx4wZg8ceewwAMG3aNERHR2P27NkYMGAAAOCFF17AmDFjJM9lMpmwdu1ahIeHAwAWL16MQYMGYf78+QgNDZVsazab8c477+DXX39FdHQ0AOC6667Dzp078emnnzLcVGb9+vWYMmUKli1bhqioKCxcuBADBgzAyZMnERwcXGH73bt3Y/jw4YiNjcXgwYPx9ddf48EHH8ShQ4dw0003yfAOyhQUlmLPkXPIL6zZL+OGIkLEf7YfhSAAzQJ9KzxWUFBQtsyAKEIURYgQARHIzCss26a8/vdaBGX/rr/+cgtq/nUrCzIqKJUqqFQqRHW5DlabA+Mf7YuI0KD6a46IyEW6dOmC/v37o3PnzhgwYADuueceDB06FEFBQcjKysKsWbOwY8cOZGdnw263o6SkBMnJyZLnuPnmm53/DgkJAXA5IJXXTCYTjEYj/P39AQCRkZHOYAMA0dHRcDgcOHnyZIVwc+bMGZSUlODuu++W1C0WC7p161Y/X4h6Jnu4WbBgAcaPH+9MlcuWLcOWLVuwcuVKTJ8+vcL2ixYtwsCBA/HKK68AKBuO++WXX7BkyRIsW7asQXsvZ7PZMWvRJqTnFMjy+jWVmnWpQi0vL69ew0p9UigUUCoVUCqVUCpVUCqVaBXeFB1ah+KmdmG4M6ojT9wjIid/Xx1WvjVK9h6qQ6lU4pdffsHu3bvx888/Y/HixXjttdewd+9eTJo0CXl5eVi0aBFatWoFrVaL6OhoWCzSQ/Rqtdr57/KfhZXVHI7qX0F6paKiIgDAli1bJIEIALRaba2e09VkDTcWiwUHDx7EjBkznDWFQoGYmBjEx8dXuk98fDymTJkiqQ0YMKDKa/HLz+UoZzQa6974P5xLzXWbYFM1AUDDpxtBKPvMpTcllMrL//1ncFkw7VG0Cmva4L0SkXsQBKHaJ/M2BoIgoE+fPujTpw/mzJmDVq1a4fvvv8euXbvw8ccfO0+7SElJQW5ubr28ZnJyMtLT0xEWFgYA2LNnDxQKBTp27Fhh2xtuuAFarRbJycmN8hBUZWQNN7m5ubDb7c5htHIhISFITEysdJ/MzMxKt8/MzKx0+9jYWLz++uv103AVTObKF1l0J4KAOo/cCIIAQQAEQQGFQvj7flk4KbtfVlcoFM5/9+neDoCA7Dwjendri5Cm/pU+d4CfHh1aBUOlUtatSSKiRmTv3r2Ii4vDPffcg+DgYOzduxc5OTno1KkT2rdvjy+++AI9e/aE0WjEK6+8Um+L9ep0OowaNQoffvghjEYjnn/+eTz22GMVDkkBgJ+fH6ZOnYqXXnoJDocDt912GwoKCrBr1y74+/tj1Ch5R8kqI/thKVebMWOGZKTHaDQiIiLC5a97a5frXP4atVFcaoZOo0bfnu0l9fS0NDhEBxSCAoJCgEJQAIIAhSBAqVQiskUQwoIDoVQq/z5MpKxw46EhIqKa8ff3xx9//IGFCxfCaDSiVatWmD9/Pu69916EhoZiwoQJ6N69OyIiIvDOO+9g6tSp9fK67dq1w8MPP4z77rsPFy9exODBg/Hxxx9Xuf2bb76J5s2bIzY2FufOnUNgYCC6d++OmTNn1ks/9U3WcNOsWTMolUpkZWVJ6llZWZWmRwAIDQ2t0fZardblxwQ7dwjHxoVPS2pu94u+W1u5OyAi8jqdOnXCtm3bKn2sW7du2L9/v6T2z3llxH8Mubdu3bpC7Y477qhQA4BJkyZh0qRJlb726tWrJfcFQcALL7yAF154odLtGxtZF87RaDTo0aMH4uLinDWHw4G4uDjn5Wb/FB0dLdkeAH755Zcqt28IZYdfpDciIiKSh+yHpaZMmYJRo0ahZ8+e6NWrFxYuXIji4mLn1VMjR45EeHg4YmNjAZRdr9+vXz/Mnz8fgwYNwrp163DgwAF89tlncr4NIiIiaiRkDzfDhg1DTk4O5syZg8zMTHTt2hXbtm1znjScnJwsWZm5d+/e+PrrrzFr1izMnDkT7du3x6ZNm2Sd44aIiMhdzJs3D/PmzZO7DZcSxMoOxHkwo9GIgIAAFBQUOCczIiIi92YymXD+/Hm0adMGOl315pihxudqn2NNfn/Les4NERFRffKyv9c9Tn19fgw3RETk9spn5C0pKZG5E6qL8tmXlcq6zWkm+zk3REREdaVUKhEYGIjs7GwAgMFg4JWrbsbhcCAnJwcGgwEqVd3iCcMNERF5hPL5zsoDDrkfhUKByMjIOgdThhsiIvIIgiCgRYsWCA4OhtXq/svieCONRiO5Qrq2GG6IiMijlC8JQ96LJxQTERGRR2G4ISIiIo/CcENEREQexevOuSmfIMhoNMrcCREREVVX+e/t6kz053XhprCwEAAQEREhcydERERUU4WFhQgICLjqNl63tpTD4UB6ejr8/PxcNsGT0WhEREQEUlJSuH6VG+Hn5n74mbknfm7uSe7PTRRFFBYWIiws7JqXi3vdyI1CoUDLli0b5LX8/f35jeuG+Lm5H35m7omfm3uS83O71ohNOZ5QTERERB6F4YaIiIg8CsONC2i1WsydOxdarVbuVqgG+Lm5H35m7omfm3typ8/N604oJiIiIs/GkRsiIiLyKAw3RERE5FEYboiIiMijMNwQERGRR2G4qYWLFy/iiSeegL+/PwIDAzF27FgUFRVddR+TyYTJkyejadOm8PX1xSOPPIKsrKxKt83Ly0PLli0hCALy8/Nd8A68kys+tyNHjmD48OGIiIiAXq9Hp06dsGjRIle/FY+2dOlStG7dGjqdDlFRUdi3b99Vt9+wYQOuv/566HQ6dO7cGVu3bpU8Looi5syZgxYtWkCv1yMmJganT5925VvwSvX5uVmtVkybNg2dO3eGj48PwsLCMHLkSKSnp7v6bXid+v5+u9LEiRMhCAIWLlxYz11Xg0g1NnDgQLFLly7inj17xD///FNs166dOHz48KvuM3HiRDEiIkKMi4sTDxw4IN56661i7969K932gQceEO+9914RgHjp0iUXvAPv5IrP7fPPPxeff/55cceOHeLZs2fFL774QtTr9eLixYtd/XY80rp160SNRiOuXLlS/N///ieOHz9eDAwMFLOysirdfteuXaJSqRTff/998fjx4+KsWbNEtVotJiQkOLd59913xYCAAHHTpk3ikSNHxPvvv19s06aNWFpa2lBvy+PV9+eWn58vxsTEiOvXrxcTExPF+Ph4sVevXmKPHj0a8m15PFd8v5X77rvvxC5duohhYWHiRx995OJ3UhHDTQ0dP35cBCDu37/fWfvxxx9FQRDEtLS0SvfJz88X1Wq1uGHDBmftxIkTIgAxPj5esu3HH38s9uvXT4yLi2O4qUeu/tyu9Mwzz4h33nln/TXvRXr16iVOnjzZed9ut4thYWFibGxspds/9thj4qBBgyS1qKgo8emnnxZFURQdDocYGhoqfvDBB87H8/PzRa1WK37zzTcueAfeqb4/t8rs27dPBCBeuHChfpoml31uqampYnh4uHjs2DGxVatWsoQbHpaqofj4eAQGBqJnz57OWkxMDBQKBfbu3VvpPgcPHoTVakVMTIyzdv311yMyMhLx8fHO2vHjx/HGG29g7dq111wUjGrGlZ/bPxUUFKBJkyb117yXsFgsOHjwoOTrrVAoEBMTU+XXOz4+XrI9AAwYMMC5/fnz55GZmSnZJiAgAFFRUVf9DKn6XPG5VaagoACCICAwMLBe+vZ2rvrcHA4HRowYgVdeeQU33nija5qvBv4GraHMzEwEBwdLaiqVCk2aNEFmZmaV+2g0mgrflCEhIc59zGYzhg8fjg8++ACRkZEu6d2buepz+6fdu3dj/fr1mDBhQr307U1yc3Nht9sREhIiqV/t652ZmXnV7cv/W5PnpJpxxef2TyaTCdOmTcPw4cO50GY9cdXn9t5770GlUuH555+v/6ZrgOHmb9OnT4cgCFe9JSYmuuz1Z8yYgU6dOuHJJ5902Wt4Irk/tysdO3YMDzzwAObOnYt77rmnQV6TyNNZrVY89thjEEURn3zyidzt0FUcPHgQixYtwurVqyEIgqy9qGR99Ubk5ZdfxujRo6+6zXXXXYfQ0FBkZ2dL6jabDRcvXkRoaGil+4WGhsJisSA/P18yCpCVleXcZ/v27UhISMDGjRsBlF3hAQDNmjXDa6+9htdff72W78yzyf25lTt+/Dj69++PCRMmYNasWbV6L96uWbNmUCqVFa4irOzrXS40NPSq25f/NysrCy1atJBs07Vr13rs3nu54nMrVx5sLly4gO3bt3PUph654nP7888/kZ2dLTn6YLfb8fLLL2PhwoVISkqq3zdxNQ1+lo+bKz8x9cCBA87aTz/9VK0TUzdu3OisJSYmSk5MPXPmjJiQkOC8rVy5UgQg7t69u8oz16n6XPW5iaIoHjt2TAwODhZfeeUV170BL9GrVy/x2Wefdd632+1ieHj4VU9wHDx4sKQWHR1d4YTiDz/80Pl4QUEBTyiuZ/X9uYmiKFosFvHBBx8Ub7zxRjE7O9s1jXu5+v7ccnNzJb/HEhISxLCwMHHatGliYmKi695IJRhuamHgwIFit27dxL1794o7d+4U27dvL7mkODU1VezYsaO4d+9eZ23ixIliZGSkuH37dvHAgQNidHS0GB0dXeVr/Pbbb7xaqp654nNLSEgQmzdvLj755JNiRkaG88YfxrWzbt06UavViqtXrxaPHz8uTpgwQQwMDBQzMzNFURTFESNGiNOnT3duv2vXLlGlUokffviheOLECXHu3LmVXgoeGBgobt68WTx69Kj4wAMP8FLwelbfn5vFYhHvv/9+sWXLluLhw4cl31tms1mW9+iJXPH99k9yXS3FcFMLeXl54vDhw0VfX1/R399fHDNmjFhYWOh8/Pz58yIA8bfffnPWSktLxWeeeUYMCgoSDQaD+NBDD4kZGRlVvgbDTf1zxec2d+5cEUCFW6tWrRrwnXmWxYsXi5GRkaJGoxF79eol7tmzx/lYv379xFGjRkm2//bbb8UOHTqIGo1GvPHGG8UtW7ZIHnc4HOLs2bPFkJAQUavViv379xdPnjzZEG/Fq9Tn51b+vVjZ7crvT6q7+v5++ye5wo0gin+f3EFERETkAXi1FBEREXkUhhsiIiLyKAw3RERE5FEYboiIiMijMNwQERGRR2G4ISIiIo/CcENEREQeheGGiIiIPArDDRF5jKSkJAiCgMOHDzeK5yEieXBVcCLyaqNHj0Z+fj42bdrkrEVERCAjIwPNmjWTrzEiqjWO3BBRo2KxWCqtW63WButBqVQiNDQUKhX//iNyRww3RFRnDocD77//Ptq1awetVovIyEi8/fbbAICEhATcdddd0Ov1aNq0KSZMmICioiLnvqNHj8aDDz6It99+G2FhYejYsaPzsND69evRr18/6HQ6fPXVVwCAFStWoFOnTtDpdLj++uvx8ccfV9mX3W7H2LFj0aZNG+j1enTs2BGLFi1yPj5v3jysWbMGmzdvhiAIEAQBO3bsqPSw1O+//45evXpBq9WiRYsWmD59Omw2m/PxO+64A88//zxeffVVNGnSBKGhoZg3b149fYWJqCb4ZwkR1dmMGTOwfPlyfPTRR7jtttuQkZGBxMREFBcXY8CAAYiOjsb+/fuRnZ2NcePG4dlnn8Xq1aud+8fFxcHf3x+//PKL5HmnT5+O+fPno1u3bs6AM2fOHCxZsgTdunXDX3/9hfHjx8PHxwejRo2q0JfD4UDLli2xYcMGNG3aFLt378aECRPQokULPPbYY5g6dSpOnDgBo9GIVatWAQCaNGmC9PR0yfOkpaXhvvvuw+jRo7F27VokJiZi/Pjx0Ol0kgCzZs0aTJkyBXv37kV8fDxGjx6NPn364O67766/LzYRXVuDr0NORB7FaDSKWq1WXL58eYXHPvvsMzEoKEgsKipy1rZs2SIqFAoxMzNTFEVRHDVqlBgSEiKazWbnNufPnxcBiAsXLpQ8X9u2bcWvv/5aUnvzzTfF6OhoyX5//fVXlf1OnjxZfOSRR5z3R40aJT7wwAOSbf75PDNnzhQ7duwoOhwO5zZLly4VfX19RbvdLoqiKPbr10+87bbbJM9zyy23iNOmTauyFyJyDY7cEFGdnDhxAmazGf3796/0sS5dusDHx8dZ69OnDxwOB06ePImQkBAAQOfOnaHRaCrs37NnT+e/i4uLcfbsWYwdOxbjx4931m02GwICAqrsb+nSpVi5ciWSk5NRWloKi8WCrl271vg9RkdHQxAEyfsoKipCamoqIiMjAQA333yzZL8WLVogOzu7Rq9FRHXHcENEdaLX6+v8HFeGn6rq5efpLF++HFFRUZLtlEplpfuvW7cOU6dOxfz58xEdHQ0/Pz988MEH2Lt3b517roxarZbcFwQBDofDJa9FRFXjCcVEVCft27eHXq9HXFxchcc6deqEI0eOoLi42FnbtWsXFAoFOnbsWKPXCQkJQVhYGM6dO4d27dpJbm3atKl0n127dqF379545pln0K1bN7Rr1w5nz56VbKPRaGC326/62p06dUJ8fDxEUZQ8t5+fH1q2bFmj90FErsdwQ0R1otPpMG3aNLz66qtYu3Ytzp49iz179uDzzz/HE088AZ1Oh1GjRuHYsWP47bff8Nxzz2HEiBHOQ1I18frrryM2Nhb//ve/cerUKSQkJGDVqlVYsGBBpdu3b98eBw4cwE8//YRTp05h9uzZ2L9/v2Sb1q1b4+jRozh58iRyc3MrveT8mWeeQUpKCp577jkkJiZi8+bNmDt3LqZMmQKFgj9GiRobflcSUZ3Nnj0bL7/8MubMmYNOnTph2LBhyM7OhsFgwE8//YSLFy/illtuwdChQ9G/f38sWbKkVq8zbtw4rFixAqtWrULnzp3Rr18/rF69usqRm6effhoPP/wwhg0bhqioKOTl5eGZZ56RbDN+/Hh07NgRPXv2RPPmzbFr164KzxMeHo6tW7di37596NKlCyZOnIixY8di1qxZtXofRORagnjlOCsRERGRm+PIDREREXkUhhsiIiLyKAw3RERE5FEYboiIiMijMNwQERGRR2G4ISIiIo/CcENEREQeheGGiIiIPArDDREREXkUhhsiIiLyKAw3RERE5FH+H2PpSinPIE3ZAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, r, cdf = ResampleCorrelations(live)\n",
    "\n",
    "model = StudentCdf(n)\n",
    "thinkplot.Plot(model.xs, model.ps, color=\"gray\", alpha=0.5, label=\"Student t\")\n",
    "thinkplot.Cdf(cdf, label=\"sample\")\n",
    "\n",
    "thinkplot.Config(xlabel=\"correlation\", ylabel=\"CDF\", legend=True, loc=\"lower right\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f9f8866",
   "metadata": {},
   "source": [
    "From Figure [\\[normal4\\]](#normal4){reference-type=\"ref\"\n",
    "reference=\"normal4\"}, we can see that the observed correlation, 0.07, is\n",
    "unlikely to occur if the variables are actually uncorrelated. Using the\n",
    "analytic distribution, we can compute just how unlikely:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "561a79d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.861466619208386e-11"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = r * np.sqrt((n-2) / (1-r**2))\n",
    "p_value = 1 - studentt.cdf(t, df=n-2)\n",
    "p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d80df7d",
   "metadata": {},
   "source": [
    "We compute the value of `t` that corresponds to `r=0.07`, and then\n",
    "evaluate the t-distribution at `t`. The result is `2.9e-11`. This\n",
    "example demonstrates an advantage of the analytic method: we can compute\n",
    "very small p-values. But in practice it usually doesn't matter."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eea3ee6",
   "metadata": {},
   "source": [
    "## Chi-squared test\n",
    "\n",
    "In Section [\\[casino2\\]](#casino2){reference-type=\"ref\"\n",
    "reference=\"casino2\"} we used the chi-squared statistic to test whether a\n",
    "die is crooked. The chi-squared statistic measures the total normalized\n",
    "deviation from the expected values in a table:\n",
    "\n",
    "$$\\chi^2 = \\sum_i \\frac{{(O_i - E_i)}^2}{E_i}$$ \n",
    "\n",
    "One reason the\n",
    "chi-squared statistic is widely used is that its sampling distribution\n",
    "under the null hypothesis is analytic; by a remarkable coincidence[^1],\n",
    "it is called the chi-squared distribution. Like the t-distribution, the\n",
    "chi-squared CDF can be computed efficiently using gamma functions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26014ba0",
   "metadata": {},
   "source": [
    "SciPy provides an implementation of the chi-squared distribution, which\n",
    "we use to compute the sampling distribution of the chi-squared\n",
    "statistic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "3e2be4ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import chi2 as chi2_dist\n",
    "\n",
    "def ChiSquaredCdf(n):\n",
    "    \"\"\"Discrete approximation of the chi-squared CDF with df=n-1.\n",
    "\n",
    "    n: sample size\n",
    "\n",
    "    returns: Cdf\n",
    "    \"\"\"\n",
    "    xs = np.linspace(0, 25, 101)\n",
    "    ps = chi2_dist.cdf(xs, df=n - 1)\n",
    "    return thinkstats2.Cdf(xs, ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7017c5e5",
   "metadata": {},
   "source": [
    "Figure [\\[normal5\\]](#normal5){reference-type=\"ref\" reference=\"normal5\"}\n",
    "shows the analytic result along with the distribution we got by\n",
    "resampling. They are very similar, especially in the tail, which is the\n",
    "part we usually care most about.\n",
    "\n",
    "We can use this distribution to compute the p-value of the observed test\n",
    "statistic, `chi2`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "bdda1ad0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = [8, 9, 19, 5, 8, 11]\n",
    "dt = hypothesis.DiceChiTest(data)\n",
    "p_value = dt.PValue(iters=1000)\n",
    "n, chi2, cdf = len(data), dt.actual, dt.test_cdf\n",
    "\n",
    "model = ChiSquaredCdf(n)\n",
    "thinkplot.Plot(model.xs, model.ps, color=\"gray\", alpha=0.3, label=\"chi squared\")\n",
    "thinkplot.Cdf(cdf, label=\"sample\")\n",
    "\n",
    "thinkplot.Config(xlabel=\"chi-squared statistic\", ylabel=\"CDF\", loc=\"lower right\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "761861dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04069938850404997"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value = 1 - chi2_dist.cdf(chi2, df=n-1)\n",
    "p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "158635d2",
   "metadata": {},
   "source": [
    "The result is 0.041, which is consistent with the result from\n",
    "Section [\\[casino2\\]](#casino2){reference-type=\"ref\"\n",
    "reference=\"casino2\"}.\n",
    "\n",
    "The parameter of the chi-squared distribution is \"degrees of freedom\"\n",
    "again. In this case the correct parameter is `n-1`, where `n` is the\n",
    "size of the table, 6. Choosing this parameter can be tricky; to be\n",
    "honest, I am never confident that I have it right until I generate\n",
    "something like Figure [\\[normal5\\]](#normal5){reference-type=\"ref\"\n",
    "reference=\"normal5\"} to compare the analytic results to the resampling\n",
    "results."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ffdd14a",
   "metadata": {},
   "source": [
    "## Discussion\n",
    "\n",
    "This book focuses on computational methods like resampling and\n",
    "permutation. These methods have several advantages over analysis:\n",
    "\n",
    "-   They are easier to explain and understand. For example, one of the\n",
    "    most difficult topics in an introductory statistics class is\n",
    "    hypothesis testing. Many students don't really understand what\n",
    "    p-values are. I think the approach I presented in\n",
    "    Chapter [\\[testing\\]](#testing){reference-type=\"ref\"\n",
    "    reference=\"testing\"}---simulating the null hypothesis and computing\n",
    "    test statistics---makes the fundamental idea clearer.\n",
    "\n",
    "-   They are robust and versatile. Analytic methods are often based on\n",
    "    assumptions that might not hold in practice. Computational methods\n",
    "    require fewer assumptions, and can be adapted and extended more\n",
    "    easily.\n",
    "\n",
    "-   They are debuggable. Analytic methods are often like a black box:\n",
    "    you plug in numbers and they spit out results. But it's easy to make\n",
    "    subtle errors, hard to be confident that the results are right, and\n",
    "    hard to find the problem if they are not. Computational methods lend\n",
    "    themselves to incremental development and testing, which fosters\n",
    "    confidence in the results."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a568fca",
   "metadata": {},
   "source": [
    "But there is one drawback: computational methods can be slow. Taking\n",
    "into account these pros and cons, I recommend the following process:\n",
    "\n",
    "1.  Use computational methods during exploration. If you find a\n",
    "    satisfactory answer and the run time is acceptable, you can stop.\n",
    "\n",
    "2.  If run time is not acceptable, look for opportunities to optimize.\n",
    "    Using analytic methods is one of several methods of optimization.\n",
    "\n",
    "3.  If replacing a computational method with an analytic method is\n",
    "    appropriate, use the computational method as a basis of comparison,\n",
    "    providing mutual validation between the computational and analytic\n",
    "    results.\n",
    "\n",
    "For the vast majority of problems I have worked on, I didn't have to go\n",
    "past Step 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14c6a1da",
   "metadata": {},
   "source": [
    "[^1]: Not really.\n",
    "\n",
    "[^2]: \"Evidence for the persistent effects of an intervention to\n",
    "    mitigate gender-sterotypical task allocation within student\n",
    "    engineering teams,\" Proceedings of the IEEE Frontiers in Education\n",
    "    Conference, 2014."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73e9a0da",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b33a1489",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:**    In Section 5.4, we saw that the distribution of adult weights is approximately lognormal. One possible explanation is that the weight a person gains each year is proportional to their current weight. In that case, adult weight is the product of a large number of multiplicative factors:\n",
    "\n",
    "w = w0 f1 f2 ... fn  \n",
    "\n",
    "where w is adult weight, w0 is birth weight, and fi is the weight gain factor for year i.\n",
    "\n",
    "The log of a product is the sum of the logs of the factors:\n",
    "\n",
    "logw = logw0 + logf1 + logf2 + ... + logfn \n",
    "\n",
    "So by the Central Limit Theorem, the distribution of logw is approximately normal for large n, which implies that the distribution of w is lognormal.\n",
    "\n",
    "To model this phenomenon, choose a distribution for f that seems reasonable, then generate a sample of adult weights by choosing a random value from the distribution of birth weights, choosing a sequence of factors from the distribution of f, and computing the product. What value of n is needed to converge to a lognormal distribution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "25edad95",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "\n",
    "def GenerateAdultWeight(birth_weights, n):\n",
    "    \"\"\"Generate a random adult weight by simulating annual gain.\n",
    "\n",
    "    birth_weights: sequence of birth weights in lbs\n",
    "    n: number of years to simulate\n",
    "\n",
    "    returns: adult weight in lbs\n",
    "    \"\"\"\n",
    "    bw = random.choice(birth_weights)\n",
    "    factors = np.random.normal(1.09, 0.03, n)\n",
    "    aw = bw * np.prod(factors)\n",
    "    return aw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "21a33acf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "\n",
    "def PlotAdultWeights(live):\n",
    "    \"\"\"Makes a normal probability plot of log10 adult weight.\n",
    "\n",
    "    live: DataFrame of live births\n",
    "\n",
    "\n",
    "    \"\"\"\n",
    "    birth_weights = live.totalwgt_lb.dropna().values\n",
    "    aws = [GenerateAdultWeight(birth_weights, 40) for _ in range(1000)]\n",
    "    log_aws = np.log10(aws)\n",
    "    thinkstats2.NormalProbabilityPlot(log_aws)\n",
    "    thinkplot.Config(\n",
    "        xlabel=\"standard normal values\",\n",
    "        ylabel=\"adult weight (log10 lbs)\",\n",
    "        loc=\"lower right\",\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "0545eb69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "PlotAdultWeights(live)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "3d0213f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# With n=40 the distribution is approximately lognormal except for the lowest weights.\n",
    "\n",
    "# Actual distribution might deviate from lognormal because it is\n",
    "# a mixture of people at different ages, or because annual weight\n",
    "# gains are correlated."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5286d50",
   "metadata": {},
   "source": [
    "**Exercise:** In Section 14.6 we used the Central Limit Theorem to find the sampling distribution of the difference in means, δ, under the null hypothesis that both samples are drawn from the same population.\n",
    "\n",
    "We can also use this distribution to find the standard error of the estimate and confidence intervals, but that would only be approximately correct. To be more precise, we should compute the sampling distribution of δ under the alternate hypothesis that the samples are drawn from different populations.\n",
    "\n",
    "Compute this distribution and use it to calculate the standard error and a 90% confidence interval for the difference in means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "49d9b077",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07803726677754952\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's the observed difference in means\n",
    "\n",
    "delta = firsts.prglngth.mean() - others.prglngth.mean()\n",
    "print(delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "c3de198b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "null hypothesis Normal(0, 0.00319708)\n",
      "0.08377070425543781 0.08377070425543787\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Under the null hypothesis, both sampling distributions are based\n",
    "# on all live births.\n",
    "\n",
    "dist1 = SamplingDistMean(live.prglngth, len(firsts))\n",
    "dist2 = SamplingDistMean(live.prglngth, len(others))\n",
    "dist_diff_null = dist1 - dist2\n",
    "print(\"null hypothesis\", dist_diff_null)\n",
    "print(dist_diff_null.Prob(-delta), 1 - dist_diff_null.Prob(delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "e81a97cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "estimated params Normal(0.0780373, 0.00321144)\n",
      "-0.015175815869865758 0.17125034942497896\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Under the alternate hypothesis, each sampling distribution is\n",
    "# based on the observed parameters.\n",
    "\n",
    "dist1 = SamplingDistMean(firsts.prglngth, len(firsts))\n",
    "dist2 = SamplingDistMean(others.prglngth, len(others))\n",
    "dist_diff_alt = dist1 - dist2\n",
    "print(\"estimated params\", dist_diff_alt)\n",
    "print(dist_diff_alt.Percentile(5), dist_diff_alt.Percentile(95))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "d175ac6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The distribution of the difference under the null hypothesis is\n",
    "# centered at 0.\n",
    "\n",
    "# The distribution of the difference using the estimated parameters\n",
    "# is centered around the observed difference.\n",
    "\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Plot(dist_diff_null, label=\"null hypothesis\")\n",
    "\n",
    "thinkplot.Plot(dist_diff_alt, label=\"estimated params\")\n",
    "thinkplot.Config(xlabel=\"Difference in means (weeks)\", ylabel=\"CDF\", loc=\"lower right\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8623c0d",
   "metadata": {},
   "source": [
    "**Exercise:** [In a 2014 paper](http://ieeexplore.ieee.org/document/7044435/), Stein et al. investigate the effects of an intervention intended to mitigate gender-stereotypical task allocation within student engineering teams.\n",
    "\n",
    "Before and after the intervention, students responded to a survey that asked them to rate their contribution to each aspect of class projects on a 7-point scale.\n",
    "\n",
    "Before the intervention, male students reported higher scores for the programming aspect of the project than female students; on average men reported a score of 3.57 with standard error 0.28. Women reported 1.91, on average, with standard error 0.32.\n",
    "\n",
    "Compute the sampling distribution of the gender gap (the difference in means), and test whether it is statistically significant. Because you are given standard errors for the estimated means, you don’t need to know the sample size to figure out the sampling distributions.\n",
    "\n",
    "After the intervention, the gender gap was smaller: the average score for men was 3.44 (SE 0.16); the average score for women was 3.18 (SE 0.16). Again, compute the sampling distribution of the gender gap and test it.\n",
    "\n",
    "Finally, estimate the change in gender gap; what is the sampling distribution of this change, and is it statistically significant?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "ef290a97",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "male_before = Normal(3.57, 0.28**2)\n",
    "male_after = Normal(3.44, 0.16**2)\n",
    "\n",
    "female_before = Normal(1.91, 0.32**2)\n",
    "female_after = Normal(3.18, 0.16**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "327daf88",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean, p-value -1.66 4.7309532320793934e-05\n",
      "CI -2.3594013558039837 -0.9605986441960161\n",
      "stderr 0.425205832509386\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "diff_before = female_before - male_before\n",
    "print(\"mean, p-value\", diff_before.mu, 1 - diff_before.Prob(0))\n",
    "print(\"CI\", diff_before.Percentile(5), diff_before.Percentile(95))\n",
    "print(\"stderr\", diff_before.sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "380056cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean, p-value -0.2599999999999998 0.1252679872068192\n",
      "CI -0.6321878891765356 0.11218788917653583\n",
      "stderr 0.2262741699796952\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "diff_after = female_after - male_after\n",
    "print(\"mean, p-value\", diff_after.mu, 1 - diff_after.Prob(0))\n",
    "print(\"CI\", diff_after.Percentile(5), diff_after.Percentile(95))\n",
    "print(\"stderr\", diff_after.sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "834ffcc1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean, p-value 1.4000000000000001 0.0018269483689769925\n",
      "CI 0.6077335793117721 2.192266420688228\n",
      "stderr 0.48166378315169184\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "diff = diff_after - diff_before\n",
    "print(\"mean, p-value\", diff.mu, diff.Prob(0))\n",
    "print(\"CI\", diff.Percentile(5), diff.Percentile(95))\n",
    "print(\"stderr\", diff.sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "bf68e90e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# Conclusions:\n",
    "\n",
    "# 1) Gender gap before intervention was 1.66 points (p-value 5e-5)\n",
    "\n",
    "# 2) Genger gap after was 0.26 points (p-value 0.13, not significant)\n",
    "\n",
    "# 3) Change in gender gap was 1.4 points (p-value 0.002, significant)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f4b59440",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
